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AD-A09 181 COMPUTER SCIENCES CORP HUNTSVILLE AL F/6 17/9
SIGNAL PROCESSOR FOR BINARY PHASE COOED CV RADAR O(U)DEC 77 8 K BHAGAVAN DAAHO3-75-A-O045
nlll
EEElEE,-EEEE
B~ 1111f2.5
1 111
1,8
11111125 1-4 1.6
MICROCOPY RESOLUTION TEST CHARTNATIONAL BUREAU OF STANDARDS 1963 A
*isc
811 26 0~
US ARMY MISSILE RESEARCH, DEVELOPMENT AND ENGINEERING LABORATORYUS ARMY MISSILE COMMAND
CLEARANCE OF MATERIAL FOR PUBLIC RELEASE
PART I
Title of Material iGNINI, POL. tog. r-0. Pfr40 ? A1L Co)u.CW RAoA&
Author(s) K, 3 GAVANOrganizational Element
Technical Report(Report Number)
Open Literature(Title of Journal)
Presentation
(Date and Place to be Presented)
This material is based upon unclassified research investigations currently being performed inthis Laboratory. There is no objection to open release on grounds of security and accuracy.Applicable security checklists, if any, were used in the review. r'-t'r ICAC: " "'JRCE i41/ - A-r A AO A d~ 6-.4/ *d b 1 4INC L4 4,,zIfZL-C4
g"Itc C;40., &~'we6&Reviewing Title
Date Organization
PART I/
CLEARANCE ACTION
(> Subject material has been APPROVED for publication and/or presentation.
Subject material has been DISAPPROVED for publication and/or presentation.
Information Office, AMICOM Date
AMSMI-R Form 92, 1 Jan 74 Previous Edition is Obsolete
IWGNALIOCESSOR FOR BINARY
PHAS CODED CW RADAR, R To fI * 0- IALA~q
I /' -; ' ] CSCITR-77/5491 (c
I I
S.CONTRACT.DAA.3-75-A-"45
"" Developed for:
i U.S. Army Missile Research and Development Command
~ Advanced Sensors Directorate- Radar Technology Branch
Redstone Arsenal, Alabama 35809
I SUBMITTED BY: APPROVED BY:
B. K. Bhagfvan EdwinxK ackson
COMPUTER SCIENCES CORPORATION
515"Sparkman Drive, NW
j Huntsville, Alabama 35806
Major Offices and Facilities Throughout the World
M-Tp!
COMPUTER4 -4 M- f- 7.1 Pz ' *' N r i. .
!
SYSTEMS DIVISION
January 25, 1978I HWS 7383
Dr. Don BurlageIDRDMI-TER
U. S. Army Missile R&D CommandRedstone Arsenal, Alabama 35809I iDear Dr. Burlage:
Enclosed are 8 copies of the CSC report entitled "Signal Processor forBinary Phase Coded CW Radar." This work was performed under Contract
I DAAH03-75-A-0045, order number CC23.
If you should require additional information, please do not hesitate to callme at 837-7200, ext. 338.
I Sincerely,
Ed Jackson
I EKJ/bc
Enclosures A
* ~RTSGA&I
I ~ ~Just lftcatl1on..__
Dstritu't ':
IAva ll l ~ i
I spcialk ' ____
F: oal .Bulg
Restn D rsnal A.Bulaaa350
PREFACE
I This report documents the work performed by Computer Sciences Corporation under
Contract DAAH03-5-A-0045. The task reported here is concerned with signal
I processing for a phase coded CW radar being developed at the Advanced Sensors
Directorate of the U.S. Army Missile Research and Development Command,
.1 Redstone Arsenal, Alabama. Computer Sciences Corporation wishes to take this
3 opportunity to express its appreciation to those that have contributed directly
and indirectly to the work reported herein, in particular, Mr. W. L. Low,
I Dr. D. W. Burlage and Mr. R. R. Boothe of the Advanced Sensors Directorate.
I
II
IIIII
_ _ _ _ _ _ _ _ _ _ _ _ _ _
TABLE OF CONTENTS
PAGE
Section 1 - Introduction.......................1-1
Section 2- Phase Coded CW Radar .. .. .............. 2-1
2.1 Introduction.-.............. ....... 2-12.2 Binary Phase Coded Signals .. .. ............ 2-12.3 Pseudo-Noise Sequences .. .. .............. 2-22.4 Performance of Phase Coded CW Radars .. .. ....... 2-7
2.5 Typical Parameter Values .. .. ............. 2-10
Section 3 -The AnalogProcessor .. ................. 3-1
3.1 Introduction .. .. ........ ........... 3-13.2 Description of the Processor .. .. ........... 3-1I3.3 Analysis of the Processor. .. ......... .... 3-33.4 Conclusions. .. .......... .......... 3-4
Section 4 - Digital Processing .. ......... ....... 4-1
4.1 Introduction. .. ...... .............. 4-14.2 Analog-to-Digital Conversion .. ........ .... 4-1
4.3 Preliminary Experiments. .. ......... ..... 4-64.4 Other Considerations .. .......... ..... 4-7
Section 5- Digital Processor Configurations .. .. ...... 5-1
5.1 Introduction.....................5-15.2 Processors Using theDecoding Approach*.. ....... 5-15.2.1 Configuration D-1lo.. ................. 5-15.2.2 Configuration D-2. .. ......... ........ 5-35.2.3 Configuration D-3 .. .. ................ 5-5
5.2.4 Configuration D-4. ....... ............... 5-55.2.5 Configuration D-5. .. ........ ......... 5-95.2.6 Configuration D-6. . ....... ....... .... 5-9I5.2.7 Configuration D-7 .. .. ............... 5-125.2.8 Configuration D-8 .. .. ............... 5-125.2.9 Configuration D-9. .. ........ ......... 5-12I5.3 Processors Using Pulse Compression .. ..... .... 5-165.4 Hybrid Processors. .. ....... .......... 5-205o5 Concluding Remarks .. ........ ........ 5-23
ii
I TABLE OF CONTENTS (Cont'd.)
I PAGE
Section 6 -Simulation and Results .. .. ........ . ..... 6-1
6.1 Introduction .. .. ..................... 6-16.2 Syntehtic Video Return. .. .. ............ 6-1I 6.2.1 Target Return. .. .. . ....... .. .. ..... 6-16.2.2 Noise...............................................6-26.2.3 Ground Clutter Return .. .. ................ 6-26.3 Processor Simulation. .. .. ............... 6-46.4 A Simulation Experiment .. .. .............. 6-46.5 Simulation Results .. .. ...................... 6-66.6 Analysis of the Results .. ............... 6-13
6.7 Conclusions . .. ........ . ......... ... .6-14
Section 7-Summary, Conclusions, and Future Efforts. .. .. .... 7-1
Appendix A -Response of the FFT Processor. .. .. ......... A-lI Appendix B -Response of Delay Line Canceller .. .. .. ....... B-1Appendix C -Coherent Integration Following MTI .. .. ....... C-1Appendix D -MTI Before and After Decoding. .. .. ......... D-1Appendix E -Output of Processors Using Decoders . .... .. ..... E-1Appendix F -Output of Processors Using Pulse Compression . . . . F-1
* Appendix G -Clutter Generation. .. ................. G-1Appendix H -Program Listings .. .. ................. H-1
LIST OF FIGURES
i Figures Page2.1 Binary Phase Modulation .. .. .... .............. 2-32.2 Shift Register Generator. .. .. ... .............. 2-52. Autocorrelation of PH Sequence. .. .. .... .......... 2-9
2.4 Magnitude Spectrum of PN Sequence .. .. ..... ........2-93.1 The Analog Processor. .. .. .... ............... 3-23.2 Target Return: In-Range Channel. .. .. ... .......... 3-43.3 Target Return: Out-of-Range Channel. .. .. .... .......3-5
3.4 In-Range Clutter. .. .. .. ................... 3-73.5 Out-of-Range Clutter. .. .. ..... .............. 3-8
4.1 Extraction of In-Phase and Quadrature Signals .. .. ...... 4-34.2 A/D Converter Characteristics .. .. ..... .......... 4-4
5.1 Configuiation D-1l.. .. ..... ................ 5-25.2 Configuration D-2 .. .. ...... ............... 5-45.3 Configuration D-3. .. .... . ............... 5-6
5.4 Configuration D-4 .................................... 5-75. Mgnitude Responses of Two Delay'Line ance1lers. .. .. ..... 5-8
5.6 Configuration D-5 .. .. ........ ............. 5-105.7 Configuration D-6 .. .. . .................. 5-115.8 Configuration D-7 .. .. .... .. ............... 5-135. Configuration D-8 .. .. ... .................. 5-145.10 Configuration D-9 .. .. .... ................. 5-155.11 Matched Filter Output With and Without Doppler Shifts .. .. .. 5-175.12 Configuration PC-i. .. .. .. .................. 5-185.13 Configuration PC-2. .. .. ...... .............. 5-195.14 Configuration H-1 .. .. .... ................. 5-21515 Configuration H-2 .. .. ...... .................. 5-22I 5.16 Uncertainty Function for a Periodic PN Sequence of Length 63. . 5-24
5.17 Magnitude at the Output of the Pulse Compression Filter . . 5-25* 6.1 Fourth Order Chebyshev Filter, Magnitude Response .. .. . .... 6-5
6.2 Hamming Weighting. .. .... . . ... .............. 6-76.3 Eighteenth Order Butterworth Filter, Magnitude Response . .6-8
6.4 Taylor Weighting................................6-96.5 Performance Comparison......................6-15
iv
LIST OF TABLES
Tables Page
2.1 Feedback Connections for Linear rn-sequences .. .. .. .. .... 2-66.1 Radar Parameters Used in Simulation .. .. .. .. ........ 6-106.2 Simulation Parameters .. .. .. .. ........ ........6-11
6.3 Simulation Results. .. .. .. ....... ........... 6-12
Iv
II,
SECTION I - INTRODUCTIONIThe need for a short range, low altitude air defense system that is capable of
operating at all times and in adverse weather conditions dictates the use of
RF devices. Passive RF systems which depend entirely on emissions from
attacking aircraft can easily be rendered useless through emission turnoff by
1the threat aircraft. Consequently, air defense systems have the need for an
active RF capability, such as a radar, in order to fulfill their task.
However, with the advent of antiradiation missiles (ARM) the susceptibility
of active radars to detection by electronic intelligence receivers and attack
radar warning receivers has become a major problem. Survivability of such a
radar can be increased by designing it so as to deny detection and classification
by the ARM receiver.
The detection performance of a radar depends on the signal energy or the
I average power. Thus for a given detection range, and hence average power, the
peak power can be reduced by increasing the pulse width, and continuous wave
(CW) transmission requires the minimum peak power. This reduces the output
power requirements of the transmitter; and, more importantly, the radar
detectability by broadband ARM receivers is reduced. In addition, CW
transmission complicates the sorting and designation process by the ARM
receiver in that the commonly used discriminants of pulse repetition frequency
and pulse width are not available. One other significant characteristic of
CW transmission is the inherent multipath problem generated by such signals.
This is due to the fact that CW signals have no leading edges while ARM receivers
rely heavily on leading edge gating to reduce multipath effects. The multipath
I problem for the receiver will be more severe if the radar employs techniques such
as intentionally illuminating the ground or other multipath scatterers.
I 1-1
II
A high gain pencil beam antenna should be used to provide a sufficient power
I density at the target with a low transmitter power level. This low power
coupled with low sidelobes on transmit provides an extremely low detectability
by a sidelobe ARM. Moreover, since the radar can be detected in the main beam
during surveillance, a small beam size confines this detectability to a small
portion of the total coverage.
When a battery of radars is operating in the area, frequency agility can be
used to complicate the designation process in the ARM receiver. Since mainlobe
detection of the rad.r is possible, beam-to-beam frequency agility makes this
detection essentially useless when the radar is not an isolated radar. The
I possibility of spot jamming by standoff jammers is virtually eliminated by
frequency agility.ISince a CW signal without modulation does not provide range resolution, it is
I necessary to increase the bandwidth of the signal by using a suitable
modulation. Selecting the type of waveform, and hence the bandwidth, is a
I compromise between potentially conflicting performance criteria such as high
I resolution, unambiguous range and doppler measurements, adequate performance in
clutter and ECM environments, low power density for increased covertness,
minimum complexity and cost of waveform generation, signal processing, etc.
Sawtooth frequency modulation and a binary phase modulated CW carrier are
I prime candidates for the radar waveform.
I The fundamental disadvantages of a phase coded CW radar are inherent to CW
radars: antenna isolation and large dynamic range caused by close-in clutter
and antenna spillover. This report documents a study of signal processors for
a binary phase coded CW radar, where a maximum length shift register generated
sequence is used for phase modulation. Following a brief review of phase
1-2
I
coded CW radars and the problems associated with such radars, several analog,
digital and hybrid signal processor configurations are proposed. The
advantages and drawbacks of each configuration are discussed. In order to
evaluate the performance of the proposed processors, digital computer
simulations of the input signal and the processors are developed. These
simulations are used to demonstrate the feasibility of digital processing in
I spite of the large dynamic range.
IIII
I
!III
I1-3
!I
SECTION 2 - PHASE CODED CW RADAR
I 2.1 INTRODUCTION
Since an unmodulated CW radar cannot resolve targets in range, some form of
modulation is required. The ability of the radar system to resolve targets in
Irange depends on the bandwidth of the transmitted modulation; in fact the range
resolution is inversely proportional to the bandwidth. Expansion of bandwidth
is achieved by modulating the CW carrier with a repetitive modulation waveform.
Two such waveforms which are most commonly used are the sawtooth frequency
modulation and binary phase coding. In addition to improved range resolution,
the enlarged bandwidth produces a lower power density thereby increasing
covertness against ARM systems that use narrow-band superhet receivers.I2.2 BINARY PHASE CODED SIGNALS
The simplest form of phase coding is the binary or the phase-reversal code in
which the phase of the carrier is shifted by either zero or 1800. The complex
representation of such a signal is given by,
0(t) = u(t) e J ° t (2.1)
where wo is the carrier frequency in radians/sec and u(t) is the modulation
J waveform. For a binary phased coded signal, the modulation waveform is of the
type
u(t) = e - J n for (n-l)8 <t < n6)
O -0or1800 n 1,2,.... (2.2)
where 6 is the code clock period.
2-1
From (2.2) it is clear that u(t) is a rectangular wave assuming values of +1 or
1 -1, and can be written as
Iu(t) = an Rn(t) (2.3)
where
IRn(t) 1 for (n-1)6 <t < n 24
10 elsewhere
I and
a _t (2.5)
I An example of a binary modulating waveform and the corresponding modulated carrier
are shown in Figure 2.1. Selection of the modulating waveform is equivalent to
choosing the coefficients a,, a2. . . . . . so that the signal has the desired range
resolution properties.
I 2.3 PSEUDO-NOISE SEQUENCES
Among the most commonly used binary modulating sequences are the Barker codes and
the pseudo-noise (PN) sequences, both of which are periodic and have similar range
J resolution properties. Barker codes suffer from a major disadvantage in that
their existence has been established only for codes with short periods. Pseudo-
Inoise sequences, on the other hand, can be easily generated using linear shiftJregister generators and have been proved to exist for all lengths of the type
N = 2n- 1 . Although pseudo-noise sequences exist for numerous other lengths, only
the linear maximum length shift register generated sequences or so-called linear
I r-sequences are considered in this study.
1 2-2
.11cI*
1 0.
2.1 r
02-3
I
ILinear maximum length sequences can be obtained from the system shown inj Figure 2.2. This shift register generator of degree n consists of n storage
elements (n stages), a clock pulse generator which generates pulses at
I intervals of 6, and a feedback logic circuit. When a clock pulse arrives, the
contents of each stage are transferred to the next stage, and the content of
the last stage is the output. The new state of the first stage is a linear
Boolean function of the previous contents of some or all the stages. For each
stage, the OFF state is symbolized by 0 and the ON state by 1. The binary
I output of the feedback logic unit is of the form
i f(xl, x2 , . . . , x.) = ClX1 ®C 2x 2 ... ®CnX n (2.6)
where xi denotes the state of the i th stage, each constant Ci is either zero or
one and the symbol (D denotes modulo 2 addition. It can be easily shown that
I the output sequence of this generator is periodic whose period is at most
i N = 2n-1 . Of the total of 2n possible feedback combinations, only a few result
in sequences whose period Is N and such sequences are called linear maximal
length sequences. The feedback connections which yield maximal length sequences
have been extensively tabulated and a part of it is shown in Table 2.1. The use
I of this table will be demonstrated with an example. Consider a 6-stage generator,
I n = 6 for which the maximum period is N = 63. The table lists three possible
feedback connections:
I (1) [6,1] which corresponds to
f(xl, x2 , x3 , x4 , x5 , x6 ) = x6 @ x1 (2.7)
(ii) [6,5,2,1] which corresponds to
f(xl, x2, x3, x4 , x5, x6 ) m x6 ® x5 (D x2 (Dx 1 (2.8)
I
'2 2-4
444
im
0.
00
II
I
I
C4
I • d
2-5
Table 2.1 Feedback Connections for Linear rn-sequences
Number of Codejstages length Feedback Connections
2 3 12,1]
13 7 13,11
4 15 [4,1)5 31 [5,21 [5,4,3,21 [5,4,2,1]
16 63 [6.11 16,5,2,11 16,5,3,21
7 127 [7,11 [7,31 [7,3,2,11 [7,4,3,217,6,4.21 [7,6,3,11 [7,6,5,2](7,6,5,4,2,11 [7,5,4,3,2,1]
8 255 [8,4,3,2] [3,6,5,3] [8,6,5,2]I (8,5,3,11 [8,6,5,1] [8,7,6,1]18,7,6,5,2,11 [8,6,4,3,2,1]
19 511 19,4)1[9,6,4,3] [9,8,5,4] [9,8,4,11[9,5,3,2] [9,8,6,51 [9,8,7,2119,6,5,4,2,11 [9,7,6,4,3.1]
[9,8,7,6,5,3 110 1023 [10,31 [10,8,3,21 [10,4,3,11 [10,8,5,1]
110,8,5,41 [10,9,4,11 110,8,4,31[10,5,3,2] [10,5,2,11 [10,9,4,21
11 2047 [11,11 [11,8,5,2] [11,7,3,21 [11,5,3,2]
111,10,3,2] [11,6,5,11 [11,5,3,1]111,9,4,11 [11,8,6,21 [11,9,8,31
112 4095 [12,6,4,1] [12,9,3,2] [12,11,10,5,2,11112,11,6,4,2,11 [12,11,9,7,6,5'[12,11,9,5,3,1) [12,11,9,8,7,4j[12,11,9,7,6,5] [12,9,8,3,2,111 [12,10,9,8,6,21
I13 8191 [13,403,11 [13,10.9,7,5,41113,11,8,7,4,11 [13,12.8,7,(,.51113,9,8.7,5.11 [13,12,6,5,4,3)113,12,11,9,5,31 113,12,11 ,5,2,11
113,12,9,8,4.21 [13,8,7,4,3,21
14 16383 (14,12,2,11 [14,13,4,21 114,13,11,91
114,6,4,21 [14,11,9,6,5,21
1 2-
II
(iii) [6,5,3,2] which corresponds to
f(x , x2 x 3, x4, x5, x6) x6 ( x5 ® x3 ( x2 (2.9)
I For a given feedback connection, different initial conditions in the shift registers
produce the same sequence with different shifts. The initial condition of all zeros
produces a sequence of all zeros and is therefore prohibited. The output of the
shift register generator is a sequence of zeros and ones which correspond to phase
shifts of zero (ai = +1) and 1800 (ai = -1).IThe fundamental properties of a linear m-sequence produced by an n-stage generator
are:
nI (I) the sequence is periodic with period N = 2 -i
(ii) in each period, the difference between the number of ones and the
number of minus ones is oneI(iii) if an m-sequence is multiplied by a shifted version of itself, the resulting
sequence is also a shifted version of the original sequence
(iv) the periodic autocorrelation is two-valued, i.e.,
N
E a I ai+k = N if i=0,+ N,+ 2N, .2.1.k~l (2.10)k= -I otherwiseI
i 2.4 PERFORMANCE OF PHASE CODED CW RADARS
The ability of the radar system to resolve targets in range depends on the
autocorrelation of the transmitted modulation. The ideal autocorrelation has a
peak at zero delay and is zero elsewhere. Consider a PN sequence of period N and
clock period 6. The code repetition interval is A - N6. The normalized
I autocorrelation of such a sequence can be shown to be periodic with period A and
2-7
has a shape as shown in Figure 2.3. Due to the periodicity of the autocorrelation,
I the power spectrum is a line spectrum and it can be shown that its envelope is
given by
U(f) 2 A (N+l sa2 (rf/B) (2.11)
j where B 1/16, except at DC where the value is A/N2 . The magnitude spectrum of the
waveform (square root of the power spectrum) is sketched in Figure 2.4. From the
I magnitude spectrum, it can be seen that the bandwidth of the signal is approximately
I. equal to B, the basic clock rate.
While the use of a veiy wide bandwidth signal offers some improved covertness
against ARM receivers which use narrowband superhet receivers, it also has several
I disadvantages in regard to the radar performance. The very high range resolution
caused by the increased bandwidth poses such problems as range-gate flythrough
I and the need for more receiver channels to cover all the desired range cells in the
i required time. A wide bandwidth signal is more likely to encounter spot jammers
spaced randomly across the operational band. The number of frequency bands
I available for frequency agility is sharply reduced by the use of wide bandwidth
signals. Finally, the large bandwidth will have an undesirable cost impact on the
I R'F portion of the radar and, in particular, the low sidelobe antenna. Although
I very large bandwidths are not desirable, the bandwidth must be sufficiently large
so as to provide good range resolution and improved performance in heavy clutter.
I The substantial benefits of a modulated CW radar are somewhat tempered by the
3 inherent drawbacks of a CW radar. Chief among these are the multipath effects,
antenna spillover and large receiver dynamic range requirements caused by close-in
I clutter. Antenna spillover can be minimized by properly shielding the receive
antenna from the transmit antenna. lhe task of designing a signal processor,
especially a digital processor, is made considerably more difficult by the large
3 dyn -iniic range requirement. 2
2-8l
|I
IIR(t)
1Ai]
I Figure 2.3 Autocorrelation of PN Sequence
I IRf)Ij
I/ \
I I -T
r B
Figure 2.4 Magnitude Spectrum of PN Sequence
T 2-9
I
II 2.5 TYPICAL PARAMETER VALUES
The following is a list of symbols and their typical values that will be used
throughout the report to demonstrate the operation of the signal processors.
Carrier Frequency: fo 10 GHz
Wavelength: X = 0.03 Meters
Intermediate Frequency: f. 30 MHz
Clock Rate: B = 5 MHz
Range Resolution: AR = 30 Meters
Code Length: N = 63
I No. of Shift Register Stages: n = 6
Unambiguous Range: Runamb = 1890 Meters
Code Repetition Period: A 12.6 p sec
Code Repetition Frequency: fr 80 KHz
I Look Time: T = 2 m sec
No. of Code Periods in One Look: K = 158
Maximum Range Rate of Interest: Vmax = 360 meters/sec
Maximum Doppler: fd = 24 KHz
Note that due to the relatively small unambiguous range, additional means such as
varying the pulse repetition rate must be employed to resolve range ambiguities.
I The existence of the dynamic range problem can be easily demonstrated by considering
a 1 m2 target at 15 KM range and a 104 m 2 fixed clutter at a 2 KM rangr. For such
a situation the signal-to-clutter ratio is
I SCR 1 104(~
S- -75 dB
2-10
In addition to antenna spillover and noise, various types of clutter must be con-
sidered in the design of a signal processor. These include in-range clutter (in the
same range cell as the target), out-of-range distributed clutter, fixed clutter such
as buildings and weather clutter.
IIIIIIIIIIII
2-I
!Ii SECTION 3 - THE ANALOG PROCESSOR
I 3.1 INTRODUCTION
The signal processor described in this c1pter is a simple analog processor and
is presented to demonstrate the principles of signal processing for phase coded
CW radars. Some of the problems associated with such a system are also elaborated.
Typical parameter values set forth in the previous chapter are used to explain the
operation of the processor. It must be noted that this processor is similar to the
Ione being used to dem~astrate the feasibility of the phase coded CW radar concept.
3.2 DESCRIPTION OF THE PROCESSOR
A simplified schematic of the processor is shown in Figure 3.1. The received RF
signal is mixed down to a convenient IF frequency fi and amplified. This signal is
then sent into 63 parallel range channels through a power divider. Each channel
contains a decoder or a code demodulator where the incoming signal is multiplied
I by the binary code but with a different shift in each channel. The target return
I may be written in the form,
gT(t) = p(t-T) cos [2 t(fi+fd) + ] (3.1)
where p(t) is the periodic code,
fd is the target doppler and
T is the range delay.
The in-range clutter has a similar form,
gc (t) - a(t) p(t-T) COB (2wtfi + tc) (3.2)
where a(t) is the low frequency amplitude variation.
3-1
'-$4
0)0I a)0)0
S-i4
0)0H -4
H a
0 0o
I 00
CC.)
I [I0apA -I-S Hd
F-4 C
oo
-'--2
II
The out-of-range distributed clutter is the sum of the returns from several range
I cells, each of the form
I gd (t) = b (t) p(t-Td) cos (21rtf i + Pd) (3.3)
I where Td t.
One of the range channels contains a decoder which has the same delay as the
target. This channel will be called the in-range channel and the other channels
I the out-cf-range channels. The decoder output due to the target in the in-range
I channel is,
rT(t) = gT(t) p(t-T)
= p(t-T) p(t-T) COS [21Tt (fi+fd) + ]
I = cos [2Tt(fi+fd) + 4](3.4)
since p(t-T) can only assume values +1 and -1.
The decoder output in an out-of-range channel due to the target is,
sT(t) = gT(t) p(t-t 1 ) ,T 0 T
= p(t-T) p(t- TI) COS [2nt(fi+fd) + 4]
= p(t-T2) cos [21t(fi+fd) + (3.5)
where T2 # 0 and use is made of the fact that a PN sequence multiplied by its
I shifted version yields the same sequence with a different shift. The output of
I the decoder is filtered by a bandpass filter with a clutter notch centered at fi.
Let the outputs of the bandpass filter be UT(t) and VT(t) when the inputs are rT(t)
I and sT(t) respectively. The spectra of the signals in the in-range and out-of-range
channels due to the target return are shown in Figures 3.2 and 3.3.
1 3-3
-8dB
I~ td I" -80 KHz
1 -36 dBf
j (a) Input Signal Spectrum
0 dB
f i.f
(b) Spectrum After Decoding
3 K~*.-~ 25 I(Hzo.i
(c) Filter CharacterisLics
10 0dB
(d) Output Signal Spectrum
Figure 3.2 Target Return: In-Range Channel
3-4
I - - 18 dB
f ~d 80 KHz
-36 dB
I(a) Input Signal Spectrum
1 -18 dB
1 -36 dBf
(b) Spectrum After Decoding
1 3 KHz 4- 5 KHz.j
1i
I (c) Filter Characteristics
(-36 dB
I (d) Output Signal Spectrum
Figure 3.3 Target Return: Out-of-Range Channel
I3-5
Note that the line spectrun of Figure 2.4 has now been replaced by a spectrum
Iof non-zero width. This is due to the finite look time of 2 msec which
corresponds to a spectral width of 500 Hz.
i • The decoder outputs due to the in-range and out-of-range clutter can be written
as,
I C (t) = a(t) cos (21rtfi + ) (3.6)
I rd (t) - b(t) p(t-T3 ) cos (21tfi + Fd) (3.7)
where T3 0 0. Let the corresponding outputs of the bandpass filter be uc (t)
and ud (t). The spectra of the clutter signals in the in-range and out-of-range
channels are shown in Figures 3.4 and 3.5.
The output of the bandpass filter is passed through a detector and then integrated.
g The output of the integrator is presented to the thresholing device for detection.
I 3.3 ANALYSIS OF THE PROCESSOR
Several observations can be made from an examination of the developments of the
I previous section. The response due to a target in an out-of-range channel is nearly
36 dB below that in the in-range channel. Therefore, the effect of range sidelobes
is negligible. Improvement in signal-to-noise ratio is derived by reducing the
I bandwidth from the original 5 MHz to 50 KHz at the bandpass filter output. This
represents a 20 dB gain in the signal-to-noise ratio. Both in-range and out-of-
range clutter can be attenuated by the notch in the bandpass filter. The notch
is 6 KHz wide corresponding to a doppler frequency range of -45 to +45 meters/sec.
Targets with radial velocities of less than 45 meters/sec cannot be detected.
II 3-6
- -- -- 18 dB
80 KHz
36 dB
(a) Input Clutter Spectrum
0 dB
II
f.
(b) Spectrum After Decoding
1 3 K~z-4 25 KHzHfl f
I(c) Filter Characteristics
It
I f
fI
(d) Output Clutter Spectrum
I Figure 3.4 In-Range Clutter
-- 3-7
.I ...
-18 dB
do -36 dB 80fz -
I (a) Input Clutter Spectrum
1 -18 dB
I (b) Spectrum After Decoding
I 3 KHzI 25 Y:Hz4'j i
I (c) Filter Characteristics
IDow- f
(d) Output Clutter Spectrum
Figure 3.5 Out-of-Range Clutter
3-8
I
The dual requirements of adequate clutter suppression and low target return
attenuation dictate the need for steep transitions at the notch. This, however,
results in a long settling time for inputs in the stop band. Thus, the transient
response due to the large clutter inputs persist for a long period of time,
thereby severely degrading the clutter cancellation performance of the processor.
The problem of long settling time may be alleviated to some extent by using a
suitable weighting scheme prior to filtering. Even with the weighting, it will
be necessary to wait for the output to settle before starting integration. The
weighting and the loss of integration time result in a reduced gain in
signal-to-noise ratio. One other problem associated with such a processor is
the reinitialization of the filter. This is because the filter must be cleared
before processing begins in the next look period. The problem of clearing is
not straightforward in the crystal filters needed for the IF bandpass filtering.
3.4 CONCLUSIONS
A simple analog signal processor was presented which uses several range channels,
IF notch filtering for clutter reduction, and non-coherent integration. The
principle of operation of the processor was explained for the case of a target in
clutter. Eventhough the processor is effective, it suffers from the disadvantage
of slowly decaying transient response and the problem of clearing the filter prior
to the next look period.
3-9
IIIo
1
ISECTION 4 - DIGITAL PROCESSING
J 4.1 INTRODUCTION
As explained in the last chapter, one of the major drawbacks of the analog
processor is the long settling time in the clutter rejection filter. An
alternative would be to employ digital processing where it is much easier to
design filters with the desired characteristics. For example, finite impulse
response or transversal filters can be designed with very short settling times.
Simple examples of such filters are the commonly used two and three pulse
cancellers. Other advantages of digital processing over analog processing
include the wide flexibility offered by digital processing and the possibility
of employing coherent integration through the use of fdst Fourier transform
(FFT) processors. However, digital processing has one significant disadvantage
compared to analog processing, it being the additional errcrs introduced due to
quantization. This chapter discusses some of the factors that must be considered
during analog-to-digital conversion or digitization.
I 4.2 ANALOG-TO-DIGITAL CONVERSION
I Analog-to-digital (A/D) conversion consists of two steps: sampling and
quantization. Sampling is the process by which the analog signal is converted
Iinto a discrete time signal. The time interval between two successive samples,
usually constant, is called the sampling interval and its reciprocal the sampling
rate or sampling frequency. While the sampled signal exists only at discrete instants
of time, the amplitude can assume a continuous range of values. Quantization
is the process where the amplitudes are approximated by a discrete set of values.
I This is necessary because in digital representation, the amplitude must be
~ represented by a finite number of binary bits (finite word length). For example
4-1 V
II
if the word length is 10 bits, then there are only 2 10 1024 discrete levels
of amplitude that can be represented. The approximation of the amplitude by a
discrete set of values introduces an error known as the quantization error
I or quantization noise.
In accordance with the low-pass sampling theorem, the sampling rate must be at
least twice the highest frequency at which the signal has a significant component.
It therefore becomes obvious that A/D conversion cannot be achieved at RF or at
IF because of the unrealistic sampling rate requirements. The signal must
therefore be shifted down to video prior to A/D conv.rsion. Since the signals
of interest are narrowband signals, the signal can be brought down to baseband,
without loss of information, by using two video channels. The in-phase and
quadrature signals can be obtained from the IF signal by simply mixing it with
sine waves at IF but with a 900 phase shift, as shown in Figure 4.1. The
in-phase and quadarture signals can be considered to be the real and imaginary
parts of a complex video signal. The spectrum of this signal is similar to the
one shown in Figure 2.4 except for a shift due to the doppler frequency. For the
set of typical parameters being considered in this study, the bandwidth of this
signal is about 5 MHz. Thus, the complex video signal can be sampled at 5 MHz
without appreciable loss oi *.nformation.
Te process of quantization can be explained with a simple example. Consider an
input signal whose range is -1 to 1 volt and a word length of 3 bits. Assuming
J linear quantization, the input-output relationship of the digitizer is as shown in
Figure 4.2, where the quantity q is called the quantization interval. It is
evident from the figure that if z is the middle of one of the steps, then any
J input in the range z-q/2 to z+q/2 yields the same output. The effect of
quantization can therefore be looked upon as the introduction of an error whose
value varies between -q/2 and q/2. To facilitate the analysis, the error is
4-2
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considered to be a random variable which is uniformly distributed between -q/2
and q/2. It can be easily shown that such a random variable has zero mean and
a variance given by
2 = q2 /12 (4.1)
If the range of the input is -V to +V volts, and if the word length is m-bits,
then it can be easily shown that
q = 2V/2m . (4.2)
In particular, if V 1 volt, then
q = 2 -(m-1) (4.3)
The dynamic range of the A/D converter is defined as the ratio of the largest
signal power to the quantization error power. Assuming a sine wave input, the
largest signal that can be converted without saturation has a magnitude of V
and a power of V2 /2. Thus, the dynamic range in dB is,
V2 /2R 1l0 logo 2R dB 0 q2/1 2
= 6.02m + 1.76
6m dB (4.4)
To gain iusight into the dynamic range problem posed by the CW radar, consider
a signal-to-clutter ratio of -70 dB. If the signal power is 1, then the clutter
variance is
a 2 = 1 0 7 (4.5)
and clutter standard deviation is
Oc 3.16 x 10 3 . (4.6)
- --- -4-5
Ifthe A/D converter input range is adjusted so that a 3a c signal is not
satratdthen
V -3o.c
3= 9.5 x 10 .(4.7)
With a 13-bit A/D converter, the quantization interval is
q =2V/213
= 2.3 volts .(4.8)
Thus, the total excursion of the target return is less than q, and if the target
return were not corrupted by clutter and noise, it is possible that the output of
the A/D converter is a constant, and that the target return will be completely
lost. One way to avoid this problem is to use a larger word length, but the word
length is limited by the 5 MHz sampling rate requirement.
4.3 PRELIMINARY EXPERIMENTS
Preliminary simulation experiments were performed to examine the feasibility of
detecting a sine wave in clutter when the signal amplitude is considerably
smaller than the quantization interval. The clutter signal included both DC
clutter and random AC clutter with Gaussian distribution and Gaussian spectrum.
A sampling rate of 5 MHz was used, and a matched filter matched to the sine wave
for a period of 2 msec was used as the detector. It was found that the sine
wave could be detected in 80 dB clutter with a word length as small as 10 bits.
Based on these results, it was inferred that digital processing is feasible for
the CW radar despite the stringent dynamic range requirements posed by the wide
disparity between the magnitudes of the clutter return and the target return.
4-6
I
4.4 OTHER CONSIDERATIONS
In addition to the quantization errors introduced during A/D conversion, roundoff
errors are introduced during every arithmetic operation. The magnitudes of these
errors depend on the word length, the type of number representation (one's
complement, two's complement, etc.) and the type of arithmetic employed (fixed
point, floating point, etc.). In the case of a complicated processor, such as
the FFT processor, these errors are substantial and must be taken into account in
the design. Another effect of the use of finite word length is the change in the
characteristics of a filter due to truncation of the coefficients. The pole-zero
structure and hence the frequency response are altered and in some extreme cases
the filter may become unstable.
It is not necessary to maintain a constant word length throughout the processor.
The word length and the quantization interval at each stage must be chosen so as
to accomodate the expected dynamic range without excessive deterioration due to
finite word length effects. The word length at each location in the processor
must be minimized from the standpoints of economy and speed of operation. It
is therefore of fundamental importance to design the processor in such a way
that the dynamic range requirements are minimized.
4-7-A
I
SECTION 5 - DIGITAL PROCESSOR CONFIGURATIONS
5.1 INTRODUCTIONISeveral digital processor configurations are proposed in this chapter. The
processors are based on two different conc-epts: decoding and pulse compression.
The analog processor described in the previous chapter uses the decoding approach.
The pulse compression method is based on converting the CW signal into a pulsed
signal followed by standard pulse radar techniques. Also included are two hybrid
processors where some analog processing is performed prior to A/D conversion. While
reading the block diagrams, it must be remembered that all the video signals are
made up of two separate signals, that is, the in-phase and the quadrature components
of the original high frequency narrowband signal.
J 5.2 PROCESSORS USING THE DECODING APPROACH
5.2.1 Configuration D-1
A schematic of this processor is shown in Figure 5.1. It -an be easily seen that
this is a video frequency equivalent of the analog processor discussed in Section 3,
I where tile clutter rejection filter has been replaced by a low-pass filter with a
I notch. This filter serves to increase the signal-to-noise ratio since it passes the
dehired signal while reducing the noise bandwidth from the original 5 Mllz to 50 Kllz.
I Because of the reduced bandwidth, the output of the filter may be resampled -t a much
lower rate, i.e., 50 KHz, without loss of information. Also, since clutter is
I attcnticited by the notch filter, the word length requirement at the integrator is much
lighter than that at the A/D converter.
If a rocursive filter is used for the notclh/LP filter, it suffers from the same
dl!.;lvintage as the analog filter in that the settling time is very large. This
I ,l'w; It att a weI[ghli, scheme befort, the filter anrd discardlg the output
9-1
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until the transient effects are negligible. If a non-recursive or a transversal
filter is used, the transient response problem is almost completely eliminated.
For example, if a L-tap filter is used, it is only necessary to discard the
first L samples of the output to avoid transients. This is usually much fewer
than the number of samples that must be abandoned when a rccursive filter is
used. In addition, if the number of taps is the same as the ratio of the input
sampling rate to the reduced sampling rate contemplated, filtering and sampling
rate reduction can be achieved simultaneously using a fixed window realization
of the transveral filter. Such a filter can be implemented with just one
multiplier and an accumulator. No signal weighting is necessary when non-
recursive filters are used. Note that when weighting is required, it can be
performed prior to decoding. Thus, the input can be weighted only once instead
of once in each channel.
5.2.2 Configuration D-2
As can be seen from Figure 5.2, this is the same as D-1 except that non-coherent
integration is replaced by coherent integration. This is achieved by using an
FFT processor with 128 input samples, and a doppler resolution of 500 Hz
corresponding to 2 msec look time. The obvious advantage of coherent processing
is the additional improvement in signal-to-noise ratio as compared to the non-
coherent case. Another advantage is the doppler resolution made available by the
FFT processor. Even if doppler measurement is not contemplated, doppler
separation may be useful in resolving range ambiguities. It i, shown in
Appendix A that the frequency response of the FFT processors feature large side
lobes. Thus, if there are two targets in the same range cell but with different
doppler shifts, the presence of the side lobes produces a large interference between
the two target returns. Tt 19 therefore neeessa y to multiply the signal by a
weighting sequence before fast Fourier transformation.
5
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5.2.3 Configuration D-3
Since the FFT processor provides frequency resolution, the notch filter has been
removed in this configuration shown in Figure 5.3. Separation of the target from
clutter is entirely based on the difference in their doppler shifts. Eventhough
transient response is no longer a problem, this processor suffers from several
drawbacks. Since there is no clutter attenuation, the word length in the FFT
processor must be large enough to accomodate the large ground clutter. The
absence of the low pass filter dictates that the sampling rate at the FFT processor
be maintained at 5 M14z. The doppler bins are still separated by 500 Hz and hence
only 100 bins are required to cover the doppler range of interest. This means that
the input to the FFT contains 10000 samples (2 m sec at 5 M1z sampling rate) while
only the first 100 output samples are required. Thus, alternate and more efficient
implementation of the FFT must be considered. The weighting requirement before FFT
is even more critical than before because of the large amount of clutter entering
the processor. The high sampling rate and the large word length requirement makes
this processor very unattractive.
5.2.4 Configuration D-4
In an effort to reduce the word length requirement at the FFT processor, a delay
line canceller is introduced in this configuration shown in Figure 5.4. Since the
clutter spectrum has components at multiples of code repetition frequency, the
delay in the canceller must be an integer multiple of the code period. It is
shown in Figure 5.5 that a delay of two code periods is desirable since it has
better gain characteristics for the doppler frequencies of interest. It is shown
in Appendix B that the transient response of a two pulse canceller can be fully
suppressed by discarding the first and the last out-put pulses. 11is corresponds to
5-
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two code periods in the beginning and at the end of the output, which is a small
portion of the total look time. Furthermore, it is shown in Appendix C that
eventhough the MTI filter gain is not the same for all. dopplers, the signal-to-
noise ratios in the various FFT doppler bins are nearly the same. However, the
signal level varies from one bin to the other and a different threshold must be
chosen for each bin. The major disadvantage of this configuration is the fact
that the FFT processor must operate with an input sampling rate of 5 !Mz.
5.2.5 Configuration D-5
Due to the presence of enormous amounts of clutter, large word lengths are required
in the processor until the clutter rejectirrn filter. It is therefore advantageous
to perform clutter suppression as early in the processor as possible. In this
configuration shown in Figure 5.6, the delay line canceller is implemented
immediately after A/D conversion. It is shown in Appendix D that the two pulse
canceller before or after decoding are equivalent provided the delay is an integer
multiple of the code period. In this case, the performance of D-4 and D-5 are
identical. However, only one canceller is needed in D-5 as opposed to one in each
range channel in D-4. Also, the early reduction in dynamic range could lead to a
more economical implementation.
5.2.6 Configuration D-6
Shown in Figure 5.7, this configuration is the same as D-3 except that a low pass
filter is introduced prior to FFT processing in order to reduce the sampling rate.
Eventhough the number of samples into the FFT processor is greatly reduced, there
is no loss in the processor gain since low pass filtering provides bandwidth
reduction and hence an increase in the signal-to-noise ratio. Due to the absence
of a clutter rejection filter, large amounts of clutter enter the FFT processor
thus requiring a large word length. Furthermore, due to the sidelobes Inherent
5-9
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in FFT processing, the large clutter component will leak into other doppler bins
unless the input is properly weighted.
5.2.7 Configuration D-7
This processor, shown in Figure 5-8, combines the advantages of configurations
D-4 and D-6 in that both a clutter rejection filter and a sampling rate reduction
filter are utilized. Here again, the low pass filter may be recursive or non-
recursive, and, if possible, filtering and sampling rate reduction may be combined
by implementing a fixed window transversal filter. Such a filter contains only
one multiplier and one accumulator in each range channel as opposed to several
multipliers for any other type of filter realization. As in the case of
Configuration D-2, weighting the input signal is required to reduce interference
between two target returns in the same range cell.
5.2.8 Configuration D-8
This is exactly the same as the previous processor except that, as shown in
Figure 5.9, the clutter rejection filter is implemented before decoding. Only
one delay line canceller is needed as opposed to 63 in Configuration D-7.
5.2.9 Configuration D-9
The main motive behind this configuration is the possibility of using a very small
word length (as small as one bit) at the decoder. In order to be able to achieve
this, the doppler information must be extracted before the decoding operation. In
this configuration shown in Figure 5.10, the incoming signal is first divided into
several doppler channels and range resolution is later achieved in each doppler
j channel. The block named compensator is a complex weighting of the signal, and it
is different for each doppler channcl as described in Appendix E. Also shown in
5
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Appendix E is the fact that this configuration is identical to D-5 in its
performance. The gain in signal-to-noise ratio is partially achieved by the
FFT processor and the rest of the gain is attained during integration following
the decoder.
5.3 PROCESSORS USING PULSE COMPRESSION
The pulse compression approach is an attempt to convert the CW signal into a
pulsed signal, so that standard pulse radar processing techniques may be used.
The pulse compression filter is a matched filter, which is matched to one period
of the code. In the absence of any doppler, the output of the matched filter
due to the target return is the same as the autocorrelation of the code. In the
presence of doppler shift, the doppler envelope is impressed on the output as
shown in Figure 5.11. However, because of the doppler mismatch (matched filter
is matched to zero doppler) the output is no longer the autocorrelation but
features larger range sidelobes, thereby reducing range resolution. The mismatch
also reduces the main peak resulting in a weaker detection performance. Two
configurations PC-i and PC-2 are shown in Figures 5.12 and 5.13, the only
difference between the two being the location of the clutter rejection filter.
It is shown in Appendix F that the output of the pulse compression processor is
not the same as that using the decoder except at zero doppler. It must be noted
that the implementation of the processors using pulse compression is considerably
simpler than those using decoders because fewer components are required. It must
be noted too that a waveform ideally suited for the decoder approach may not be
suitable for the pulse compression approach and vice versa.
I
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5.4 HYBRID PkOCESSORS
The principal limitations of the digital processors are the conflicting require-
ments of high sampling rate and large word length, while their advantages are
flexibility and easy realization of coherent integration using FFT processors.
The hybrid processors are designed to maintain these advantages while overcoming
some of the drawbacks of digital processing by performing a portion of the
processing before A/D conversion. Coherent integration capability of digital
processing is utilized in Configuration H-i shown in Figure 5.14. *Because of
clutter attenuation and bandwidth limiting by the analog filter, both the
requirements of sampling rate and word length are made less stringent. The
analog filtering may be performed either at video on the in-phase and quadrature
signals or at IF. If IF filtering is used, the in-phahe and quadrature components
must be extracted prior to A/D conversion. The main disadvantage of this processor
is the same as that of the analog processor described earlier, that 4s, the loss in
achievable processor gain due to the large settling time of the notch filter.
This problem can be alleviated by using Configuration H-2, shown in Figure 5.15,
where clutter rejection is performed in the digital portion. This is accomplished
by the use of a delay line canceller in which the transient response problems are
completely avoided. However, since no clutter attenuation takes place before A/D
conversion, large word lengths are required to accomodate the expected dynamic
range. This problem is not as severe as in the all-digital processors because of the
availability of A/D converters with large word lengths at lower sampling rates.
It must be noted here that eventhough the sampling rate has been reduced, the
number of A/D converters has been increased from one to one in each range channel.
Superiority of hybrid processing is accompanied by a loss In flexibility due to
the fact that the analog portion of the processor cannot be easily adapted to any
changes in the waveform or other parameters.
!' 5-20
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5.5 CONCLUDING REMRKS
The principal attractions of digital processors are the flexibility they offer and
the possibility of obtaining filter characterics which could not be realized by
analog systems. In this chapter, several configurations were proposed as possible
candidates for digital processors in a phase coded CW radar. Each processor is
based on one of two different concepts: decoding and pulse compression. Even-
though several of the configurations are mathematically equivalent, their detection
performance may vary because of the nonlinearity inherent in quantization.
Therefore, each of th- processors must be analyzed in detail to minimize the
cost for specified performance levels.
Figure 5.16 shows the uncertainty function for a PN sequence of length 63, a clock
rate of 5 MHz and a look time of 2 m sec. As can be seen the signal exhibits the
desirable properties of good range and doppler resolution and small range side lobes.
These properties can only be attained if the processor consists of a bank of filters
each matched to a different doppler shift. Configuration D-3 is, in fact, such a
processor while the other decoder configurations using coherent integration are
close approximations. However, the processors using pulse compression produce
large range side lobes because of the doppler mismatch in the pulse compression
filter which is matched to zero doppler. This can be seen from Figure 5.17 which
shows the magnitudes at the output of the pulse compression filter for various
dopplers. The input to the pulse compression filter is a doppler shifted phase
code at zero range delay. At zero doppler, the range side lobes are exactly the
same as in the decoder approach, since the pulse compression filter is exactly
matched to the input waveform. However, as the doppler shift of the input increases,
the mismatch produced manifests itself in large range side lobes and a reduced main
lobe. While this effect is not pronounced at small doppler shifts, the degradation
is unacceptably large at higher doppler frequencies. It must also be noted that the
5-23
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range side lobe structure depends upon the initial shift in the code (initial
contents of the shift register) unlike in the decoder approach. The severity
of the range side lobes is entirely dependent upon the modulating waveform
and it is necessary to analyze several waveforms in order to select one which
is suited for the pulse compression processor.
The main factor that restricts the performance of a digital processor is the
effect of finite word lengths. This effect can be reduced by expanding the
word length, but an upper limit on the word length is imposed by the high
sampling rate necessary to avoid errors due to aliasing. In an effort to
reduce the sampling rate required, two hybrid processing schemes were proposed
where some flexbility is sacrificed by performing a portion of the processing
before analog-to-digital conversion.
5-26
IJ
ISECTION 6 - SIMULATION AND RESULTS
6.1 INTRODUCTION
In order to study the performances of the various configurations, digital
computer simulations of the processors have been developed. To facilitate a
Monte Carlo analysis of the performance, computer programs have also been
developed to generate samples of synthetic video return including ground clutter,
noise and return from a single moving target. All the programs are written in
FORTRAN compatible with the CDC 6600 computer system. Program listings are
included in Appendix I.
6.2 SYNTHETIC VIDEO RETURN
Samples of the video return are normalized so that the power in the target return
is unity. It is assumed that the sampling rate is equal to the clock rate of the
PN sequence. The total return includes contributions due to the target, noise
and clutter.
6.2.1 Target Return
The target is assumed to be a moving target with a doppler frequency fd and a
range delay corresponding to k clock periods. Thus, if the target range is R and
the range resolution is AR, then the range delay in clock periods is
k = Int (R/AR) modulo (N) (6.1)
where Int (.) denotes "integer part of" and N is the length of the code. If the
set {p(i)} denotes samples of the periodic code, then the ith sample of the in-
phase and quadrature components of the target return are given by
6-I
. .. . .. ..W - ° mmm m mm ( m
I
Ixl(i) = p(i-k) cos (2 fffdi 6 + ,t ) (6.2)
xQ(i) = p(i-k) sin ( 2 nfdi6 + t ) (6.3)
where t is a random phase which is constant over a look period. As can easily
be seen, the total power in the target return is unity.
6.2.2 Noise
If the required signal-to-noise ratio in dB is SNR, then the total noise power
is
a2 = 10-0.1 SNR (6.4)
This noise power is divided equally between the in-phase and quadrature channels.
The noise samples in each channel are assumed to have a Gaussian distribution with
zero mean and a variance of a2 /2. The samples are independent of one another and
the noise sequences in the two char:nels are assumed to be independent of each
other.
6.2.3 Ground Clutter Return
If the required signal-to-clutter ratio in dB is SCR, then the clutter power is
A2 = 10-0.1 SCR . (6.5)
Ground clutter return is assumed to have a steady or DC component and a random
fluctuating or AC component. Tle i t h sample of clutter return in the in-phase
and quadrature channels are generated according to the following equations.
cl(i) = A p(i-k) [go cos 4 , + ga fl(i)] (6.6)
cQ(i) = A p(i-k) [go sin 4)c + ga fQ(I)1 (6.7)
6-2
II
where {p(i)} is the periodic code sequence,
k is the range delay of the clutter source in units of clock period,
_ ; 2 is the DC component of the clutter power,
l+M
m2 is the clutter DC-to-AC power ratio,
= A 1 ; 2g 2 is the AC component of the clutter power,ga (i + 2 )
Yc is a random phase angle which is constant over a look period,
and {fi(i)} and {fQ(i)} are samples of the AC clutter component. The random
sequences {f1 (i)} and {fQ(i)} are assumed to have a Gaussian distribution with
zero mean and unit variance and the two sequences are independent of each other.
However, each sequence is assumed to be highly correlated and to have a Gaussian
spectrum with zero mean and a standard deviation of 0c Hz. Samples of the
random clutter component are generated by introducing the desired correlation to
an independent random sequence. This is accomplished using a linear system, and
the process is explained in Appendix G.
Various types of clutter may be produced by proper use of the above procedure.
Pure DC clutter resulting from static reflectors such as buildings czn be obtained
by setting ga to zero and go to one. Antenna spillover can be simulated as a DC
clutter with zero range delay, that is, k=O. Distributed clutter is generated by
adding the clutter returns from several range cells. The return from each range
cell must take into account the power variation according to the inverse of the
fourth power of range, and the delay corresponding to the particular cell.
6-3
I
6.3 PROCESSOR SIMULATION
Since the proposed digital processors contain similar components but in different
orders, each of the blocks was seperately simulated. This includes A/D converter,
decoder, pulse compression filter, delay line canceller, weighting function, digital
filter for clutter rejection and sampling rate reduction, FFT processor, and non-
coherent integrator. Simulation of the digital processors is not complete in that
only the quantization errors due to A/D conversion can be simulated. Finite word
length effects elsewhere in the processor including the fast Fourier transformation
have not been included. The notch and/or sampling rate reduction filter is assumed
to be a recursive filter and is implemented as a cascade of second and first order
sections to minimize the effects of coefficient quantization. Each of the first and
second order sections is realized in the canonical structure. It should be noted
that processor Configuration D-9 cannot be simulated with the programs that have been
developed because of its many differences in comparision with the other configurations.
6.4 A SIMULATION EXPERIUENT
The simulations developed were exercised for a typical set of parameters. The object
of the experiment was twofold: (i) to study the feasibility of digital processing
when the target return is much smaller than the quantization interval of the A/D
converter and (ii) to compare the performance of a digital processor with that of
the analog processor described in Chapter 3.
Configuration D-8 was chosen as the candidate digital processor. Figure 6.1 shows the
magnit,:de response of a fourth order Chebyshev low pass filter used for sampling rate
reduction. This filter has 5 dB ripples in its pas hand but, using the same
argument as with the delay line canceller, this should not affect the output signal-
to-noise ratio due to the narrow doppler filters provided by FFT processing. The
output of this low pass filter was resampled at 80 K11z as opposed to 64 Kh1z sugges ted
6-4
I . I:* I
I . -
I N
I -
- . I. . * ~-J -[i72 I I .
- . .w-----------------------------------
--------------------------------1... I~. -
* -I -- ~ --- . I.. -
I . . - -*-. . F
I -
. - F'4 1~ -- F -
* I ~ 2
F . - I -
I Lt-~
- F- -~* - -~ . F - - -
) - * - -- *-I----~~- -~tJ-
- F -~-
-- .x+ ---------- ______
- . I - - ~ - F---i----I -- ;--- F __________
F - I . ____ -
---------------- ,-~~-'-I--.- - -- -- -~ . - --
-- -I
F-! __
- - . I * -
- .- II - -
_ - ---I -- --.-------- c'J_ ___
-- - t . - f* -- . .-.- - - -
I-.
- o Li-----* I K *
-.-- . . -
--------------------------------I-i . F
~0
#4) -~ Q - - ~0'.0
-- I
"(I
('-5
I
in Figure 5.9. The input samples to the FFT processor were weighted with a
Hamming function shown in Figure 6.2. The simulation of the analog processor
is exactly similar to Configuration D-1 with one difference. The non-coherent
integration is performed at the original sampling rate instead of a reduced
sampling rate to provide a better simulation of the analog integration.
The analog notch/low pass filter was modelled by a 10th order Butterworth low
pass filter in cascade with an 8th order Butterworth high pass filter. The
magnitude response, shown in Figure 6.3, was found to be a satisfactory approximation
to the response of the analog filter. Assuming a lcrk time of 2 milliseconds, a
non-symnetrical Taylor weighting function (with n = 10 and -50 dB sidelobes), shown
in Figure 6.4, was applied to the input prior to filtering. As explained in
Chapter 3, the transient response must be allowed to settle down before starting
integration. In this experiment, the non-coherent integration was started after
1.33 milliseconds, i.e., out of the 2 milliseconds look time, integration was
performed only over 0.67 millisecond.
Table 6.1 shows the radar parameters used in the simulation. For these set of
typical radar parameters, the signal-to-noise ratio at the input to the receiver
can be computed to be -20 dB using the radar range equation. A complete list of
other simulation parameters is given in Table 6.2.
6.5 SIULATION RESULTS
The outputs in range channels 32, 28 and 36 were computed for both the analog and
the digital processor using the parameters given above. These channels represent
the in-range and two out-of-range channels all of which contain clutter and noise.
A Monte-Carlo analysis of 30 samples wam-, performed to determine the means and
variances of the outputs. These results are given in Table 6.3 where the output
6-6
* - - -
* --
0
tot
.4 -4 __6-7
T-1~
-i-F
O'EI 0r4
I I
____~~~~..... ..__ _ _ _ __ 1 _ _
____ ___ ______ ___ {~ T ____6-8-
I I::'
I I:
~F ~~17 -
4 T
__ __ -} .~I-- - - T r
I II I
___ ___ p Lr~~-4
i122~...iI ____I I 77>i.i ---. __
_ I i II__ 1 __ __ 1 .. 2
o ~~~~1 __ ___
___________ ___________ p j ________ . .
_ _ _ I_ T _
I I IJ. 1 ___ ____
-I 4~i~
___ ___ ___ ___ ___ 12 ____
_______ _______ _______ _______ _______ I I __________
I T I
) ~1 I
__ _ __ __
F 0*
T I
I I I
:1.....1~ ___ ~1 -
I I
]I Lf.~
%m.) I
.11 F I 01
...........................i*.......1...
6-9
Table 6.1 Radar Parameters Used in Simulation
Transmitted Power 10 watts
Transmit Antenna Gain 38 dB
Receive Antenna Gain 40 dB
Wavelength (X-band) 0.03 meter
Target Cross Section (Steady) I sq. meter
Target Range 15000 meters
Length of PN Sequence 63
Clock Rate 5 MHz
Code Period 12.6 sec.
Target Range Rate 240 meters/sec.
Doppler Frequency 16 KHz
Receiver Bandwidth 5 MHz
Noise Figure 5 dB
Losses 9.5 dB
6-10
Table 6.2 Simulation Parameters
Target: 1 sq. meter steady target in range cell 32
In-range Clutter: Signal-to-clutter ratio = -70 dB
DC-to-AC power ratio = 0.8
Out-of-range Clutter: Signal-to-clutter ratio = -70 dB
DC-to-AC power ratio = 0.8
Appears in range cell 28
Fixed Clutter: Signal-to-clutter ratio = -60 dB
Appears in range cell 32
Clutter Parameters: Wooded Terrain
Wind Velocity = 18 knots
Clutter doppler spread a F = 8 Hz
Noise: Signal-to-noise ratio = -20 dB
Sampling Rate: 5 Mbz
A/D Converter Input Range: -18000 to 18000 volts
Look Time: 2 milliseconds for analog processor
1.65 milliseconds for digital processor
Integration: Square law detection and integration for 0.67
millisecond in analog processor
128 sample FFT in digital processor followed
by a square law detector
6-11
7 -- N
Table 6.3 Simulation Results
Range Bin Range Bin Range Bin28 32 36
Mean 8692.04 17612.51 8472.89Analog Processor _____ _____
Variance 4.6585x106 6.5340x106 1.4319x,06
Mean 0.5044 33.0759 0.4370Digital Processor_______
36 BitsVariance 0.1752 29.5580 0.1726
Mean 1.2152 32.4057 0.9593Digital Processor _____
10 BitsVariance 2.9316 91.9885 0.5703
Mean 0.5493 33.3664 0.4443Digital Processor
13 BitsVariance 0.1910 29.4330 0.2020
6-12
of the digital processor corresponds to the output in the doppler channel in
which the target is present. The digital processor was analyzed for three
different A/D converter word lengths: 36 bits, 10 bits and 13 bits. Thle 36
bit word length was included for validation purposes since the quantization
effects at this word length are inconsequential.
6.6 ANALYSIS OF THE RESULTS
In the case of the digital processors, tie mean of the output is the variance before
detection since a square law detector is being used. Since the original bandwidth
is 5 MHz and the detection bandwidth is 620 11z (based on the look time), the expected
gain in signal-to-noiqe ratio is 39 dB. Thus the expected signal-to-noise ratio at
the output without quantization effects is 19 dB. Using the results for 36 bits and
range bins 28 and 32, it can be shown that the signal-to-interference ratio is 18 dB.
This agrees with the predicted value and suggests that the large amount of input
clutter has an insignificant effect on the output.
With a 13 bit A/D converter, the peak signal amplitude is four times smaller than
the quantization interval corresponding to a signal-to-quantization error ratio of
-5 dB. The effect of this is to decrease the input signal-to-noise ratio from -20 dB
to -20.13 dB. The results show that the output signal-to-noise ratio is 17.75 dB,
which is a fraction of a dB below that for the case where the word length is 36 bits.
It should be noted that with il bits, the standard deviation of the input noise is
about twice the quantization interval.
When the word length is reduced to 10 bits, the input noise standard deviation is
one-fifth the quantization interval. The corresponding signal-to-quantization
error Is -23.15 dB which has the effect of increasing the input. signal-to-noise
ratio from -20 dB to -24.7 dB. From the rest.,ts it cal be shown that the output
signal-to-noise ratio is 14 dl1 which is 4 d1 less than the unquanLized case.
6-13
Due to the noncoherent integration and the fact that clutter residues persist
despite the weighting and delaying the start of integration, it is not
straightforward to interpret the signal-to-interference ratio at the output of
the analog processor. The most desirable way to aiialyze this processor is to
perform an extensive Monte Carlo analysis to ascertain the probabilities of
detection and false alarm. Such a simulation requires an enormous amount of
computation. For purposes of this preliminary comparison, probabilities of
detection and false alarm were computed by using approximate probability density
functions. Probability densities with and without a target were approximated by
a non-central and a central chi-squared distribution respectively. The
appropriate parameters of these distributions were derived using the results of
the simulation. Then, by varying the threshold, a curve of probability of false
alarm versus probability of detection was developed for each processor. This
set of curves is shown in Figure 6.5.
6.6 CONCLUSIONS
The results of the simulation show that it is indeed possible to extract the
signal using a digital processor whose word length is such that the signal is
considerably smaller than a quantization interval. Furthermore, detection is
possible even when the input noise standard deviation is smaller than the
quantization interval. Despite the large transients caused by clutter, it is
shown that the analog processor can be used if a proper weighting function is
used. However, for the set of parameters used, a look time of 2 milliseconds
does not seem to provide an adequate detection performance by the analog
processor. Finally, for a given look time, the digital processor gives a
considerably better detection performance. This is attributable to the absence
of undesriable transients and the use of coherent integration.
6-14
-.- -1 -
TI rIT
C' D
- ~ ri 0!P ' Jo I I- 1 (0
C '--V0
SECTION 7 - SYMMARY, CONCLUSIONS, AND FUTURE EFFORTS
The principal problem that must be addressed in designing a signal processor for
a phase coded CW radar is the large dynamic range requirement that is caused by
antenna spillover and close-in clutter. Since the clutter return could be 60-80 dB
over the target return, the clutter rejection filter must be designed to have a
very short settiing time. Otherwise, the transient response due to the large
clutter return will have the effect of reducing the signal-to-interference ratio
thereby deteriorating the detection performance of the radar. Since digital
clutter rejection filters, such as delay line cancellers, can be designed to have
very short rettling times, the possibility of using digital processing must be
given serious consideration . Another attractive feature of digital processors is
that they are considerably more flexible than analog processors. The main
disadvantage of digital processing is tihe introduction of quantization errors
due to the finite word length.
r
For a given dynamic range requirement, quantization errors can be reduced by
increasing the word length. But the high sampling rate made necessary by the use
of a wideband signal imposes a limit on the word length that can be obtained from
currently available analog-to-digital converters. At the dynamic range and
sampljng- rate of interest in this application, the largest word length aviilable
has a quantization interval which is much bigger than the amplitude of the target
return. This problem can be partially alleviated by using hybrid proce-sors
where some flexibility of digital processing is sacrificed to relax the stringent
and conflicting requirements of large dynamic range and high satupling rate.
Several analog, digital. and hybrid configurations were proposed in this report
as candidates for signal processors in a binary phaise coded (MW radar. Synthetic
7-1
input signals including returns due to clutter, target and noise were used along
with digital computer simulations of the processors to show the feasibility of
digital processing. It was shown that is was possible to dcLect a target when
the target return is much smaller than the quanti.-ation interval of the A/D
converter. The target was detectable even when the input noise was smaller than
the quantization interval. It was also shown that the analog processor could be
used if the transient response of the clutter rejection filter were controlled by
modifying the input signal by a suitable weighting function.
It must be remarked that this study is incomplete aid that the most significant
conclusion is that digital processing is feasible despite the rigid sampling rate
and dynamic range requirements. T7he following is a partial list of topics that
must be investigated before selecting the optimal processors.
1. Effects of arithmetic roundoff and quantiziion of filter coefficients
should be studied. Since no adequate theoretical tools are available,
this must be performed through computer simulation.
2. Each of the configurations should be analyzed to determine dynamic
range requirements at different stages of the processor. This is
required in order to be able to use the available word length in the
most efficient manner.
3. The simulation programs must be modified for use in the SEL computer
and/or the All 120B array processor. This will facilitate the
computation of detection and false alarm probabilities using an
exhaustive Monte-Carlo analysis.
4. The fen;;ib-lity of using a fixed window transvera] filter for salmpling
rate reduction mu.st be investigated. This is important since such a
7-2
filter can be implemented with much less hardware than a recursive
filter.
5. Adaptive thresholding by the use of constant false alarm rate (CFAR)
processors should be examined. This techinique is useful in avoiding
false alarms in the presence of large unc>::,.ted int.r. crence sources.
6. MTl filters other than delay line cancell,-s cm . u: ,,d for clutter
rejection. These can be of either recursive or ntn-rcurc:ive variety.
In the Ltter case proper initialization is rw <cs to avoid transient
effects.
7. The study must be expanded to include the effects of bandlimiting on
the code and the effects of scanning modulation where a continuous
scan is used instead of a step scan.
8. The processor must be modified to operate in clutter environments
other than ground clutter. This entails the use of notch filters for
rejection of weather clutter and chaff.
9. The typical ,,t of parameters used in this study yields an unambiguous
range of 18F90 :,tera. One way to remove this ambiguity is to increase
the lentli of the I'N :equence.
This, however, reducs the code repetition frequency which in turn
decreases the separationi between blind speed!; produced by the clutter
rejection filter. To avoid blind speeds, some method analogous to
staggered PRF must be employed. The extension of staggered PRF to phase
coded CW radars is not obvious and needs further investigation. The
enlalrged ]eng th of the sequence also increases the number of range channels
7-3
and hence the complexity of the processor. Therefore, alternate
schemes for unambiguous range measurement must be examined.
10. The maximum length binary sequence does not seem to be ideally suited
for the pulse compression approach. It is therefore necessary to
study other types of waveform to find one which provides a
satisfactory performance with the pulse compression processor. It
must be remembered that the pulse compression processors are
considerably easier to implement than those using decoders.
11. Even though some of the digital processor configurations are
mathematically equivalent, their performances may not be identical
because of the nonlinearity involved in quantization. It is
therefore necessary to evaluate all the configurations to select a
processor which offers the best compromise between performance and
cost of implementation.
7-4
APPENDIX A
RESPONSE OF THE FFT PROCESSOR
Let the input to the processor be a sampled complex exponential,
xn -exp (21r j f n A), n=O, 1, . , N-I (A.1)
where
f = frequency
N = number of input samples,
and A = sampling interval.
The frequency resolution of the FFT processor is the reciprocal of the input
duration, i.e.,
F = 1/NA, (A.2)
and the kth output sample corresponds to a frequency kF. The frequency response
of the kth frequency bin will be defined as the magnitude of the kth output
sample as a function of the input frequency f. This output sample is given by
N-1
k (f) = -N E xn (A.3)
n=O
where
exp (-2nj/N) (A.4)
Using (A.1) and (A.2), (A.3) reduces to
] N-1.
Xk (f) = N N2jAf (A.5)
A-1
y" ,
where
fr = f - k F. (A.6)
Tile summation in (A.5) is a finite geometric series and can be written as
Xk(f) exp (2rj N Afr) -1 (A.7)k~f N exp (2Trj -fr) -1
The above equation can be rearranged to give
Xk(f) 1 sin lrN Afr (A.8)N Isin ir A frI
For large values of N and small values of fr' the frequency response can be
approximated as,
Xk(f) sa (IT NA fr) (A.9)
where the function sa(x) denotes sin x/x.
An examination of the above expression reveals the following properties:
(i) the response of the kth bin is centered at frequency kF,
(ii) the frequency response contains large sidelobes, and
(iii) there is considerable overlap between the responses of neighboring
bins. In fact, at the frequency where the two responses c-o,;s,
the gain is about 4 dB below the maximum gain.
If the input is an independent, zero mean noise sequence with variance 1, it can
be easily shown that the output in each bin of the FFT processor is a zero mean
noise whose variance is 1/N. Since the input signal-to-noise ratio is unity, the
gain in signal-to-noise ratio is the same as the output signal-to-noise ratio
which is,
A-2
SNR0 = kf 2M11N
=N [sa (ft N A frjJ (A. 10)
A- 3
APPENDIX B
RESPONSE OF DELAY LINE CANCELLER
The input is assumed to be a finite duration signal,
r(t) = x(t) W1 (t) (B-1)
where x(t) is an infinite duration signal and wl(t) is a window function given
by
wI(t) 1 f-r 0 <t< T
= 0 otherwise - (B.2)
The output of the two pulse delay line canceller is
y(t) = x(t) - x(t-A) (B.3)
and the impulse response of the filter is
h(t) = 6(t) - 6(t-A) (B.4)
The output can therefore be written as
y(t) = x(t) wl(t) - x(t-A) wl (t-A) (B.5)
and exists in the interval O<t< T + A.
To avoid the effects of transients, a portion of this signal is discarded.
Specifically, two segments of y(t) in the intervals O<t<A and T<t<T + A arc not
B-i
used in further processing. This is identical to multiplying y(t) by a window
function w2 (t) such that,
w2 (t) = 1 for A<t<T
- 0 otherwise (B.6)
But from the definitions of wl(t) and w2 (t), it can be easily seen that
wl(t) w 2 (t) = w2 (t), (B.7)
and wl(t-A) w2 (t) = w2 (t) (B.8)
Therefore the final output is
z(t) = [x(t) - x(t-A)] w 2 (t) (B.9)
Thus, the effect of discarding the transients is equivalent to passing the
infinite duration signal through the canceller followed by windowing. The
importance of this is in regard to ground clutter. If the transients ace not
discarded, the effect of finite observation time is to smear the spectrum of the
input signal. Tiierefore, the low frequency ground clutter spectrum expands into
the passband of the filter. Discarding the transients improves clutter rejection
performance since spectrum smearing takes place after the filtering which is
designed to attenuate the low frequency clutter components and, in particular, to
suppress the DC clutter completely. It must be noted that this analysis is valid
only for step scan systems since the input amplitude has been assumed constant.
The effect of discarding transients is not so great in continuously scanned
systems since the antenna pattern automatically produces a spectral widening of
the input signal.
B-2
APPENDIX C
COHERENT INTEGRAT ION FOLLOW ING MT I
The input sampled signal is assumed to be of the form,
r(n) = x(n) + p(n), n = -1, 0, 1, N-i (C.1)
where x(n) = exp(2-rj f nA) (C.2)
and p(n) is a zero mean, independent noise sequence with unit variance. Notice
that the input signal-to-noise ratio is unity. It is assumed that this signal
is passed through a two pulse canceller followed by an FFT processor. The signal
component of the output of the two pulse canceller aftier discarding transients is,
y(n) = x(n) -x(n-l)
= exp(Zrrj f nA) [l-exp(-2rj fA)I (C.3)
If this sequence is passed through an FFT processor, the kth output sample is
Y~k) = N-1 nk(c)
n0O
where w = exp(-2ij/N)
From (C.3) and (C.4), one can write
N-1Y(k) [l-exp(-2rj fA)] -1 , exp(2ij f nA)wnk
N E..n0O
= (-exp-27j f A)] 1N- exp(2-ffj n Afr) (C.5)
n=O
C-1
where f r fkF (C. 6)
and F l /NA. (C.7)
It follows that,
y(k) =2 sinr fA sin 7T N A f (C.8)=1 Nsin 7T A fr'
The noise samples at the output of the canceller are
m(n) = p(n) -p(n-l), n0O, 1, .. ,N-i. (C.9)
Obviously, this is a zero mean noise sequence but is not an independent sequence
due to the correlation introduced by the canceller. In fact, it can be easily
shown tha t
Efm(n)i(i)] = 2 if n =i
- -1 if In-iK 1
= 0 otherwise (C.10)
where E[.1 denotes statistical expectation.
The kth output noise sample of the FFT processor is,
N-1M(k) m(n)w~ (C .11)
n0O
This noise sample has zero mean and a variance given by,J
E[ IM(k )12] 1 N2 E m(n)m(i)wkn wk (C.12)
C-2
Using (C.1O), the above equation can be reduced to
E[I~ k)1 ] 1 [2 E 2(n )+n ( n-,w-k+m ( m ( l~ w k]N I
1 k -k
N2 [2N -N(w +w )
=4 sin2Qnik FA)/N. (C.13)
The total gain in signal-to-noise ratio, which is the same as the output
signal-to-noise ratio is,
SN0= [y(k) 2E[1N k) 2
4 sin2 7f A [sin 7NA '1r(.144 sin2 (ikFA)/N LNsin n A fri c.4
In the doppler bin containing the target, f kF and for large values of N,
(C.14) can be approximated as,
SNR 0 N [sa(7r N A fr)]2 (C.15)
which is the same as that obtained by coherent integration without the delay
line canceller. Thus, introducing a two pulse canceller ahead of the FFT
processor has little effect on the improvement in signal-to-noise ratio.
However, the signal levels in different frequency bins are not the same and
each bin maust be assigned a different threshold which takes into account the
frequency response of the delay line canceller.
C- 3
APPENDIX D
MTI BEFORE AND AFTER DECODING
The received signal consists of K periods of the code and there are N samples il,
each code period. These samples are denoted as r(i), i=O, 1, . . , KN-I
Let this set be partitioned into K segments of N samples (one code period) each
such that,
rk(n) = r(kN + n) for k = 0, 1, . , K-1,
and n = 0, 1, . , N-1. (D.1)
The output of the decoder in rangc channel corresponding to a delay of m samples
is obtained by multiplying r(i) by a periodic repetition of Cm(n) where C m(.)
represents a period of the code shifted by m samples. Thus, if the output y(i)
is also partitioned as above, then
Yk(n) = rk(n) Cm(n) (D.2)
If this sequence is then passed through a two pulse canceller whose delay is an
integer multiple of the code period, i.e., the delay is pk samples, the output of
the canceller in partitioned form is
zk(n) = Yk(n) Yk-p(n)
= [rk(n) - rk-p(n)] Cm(n) (D.3)
If the MTJ is performed before decoding, the output of the two pulse canceller
in partitioned form is
Xk(n) = rk(n) - rk-pn) (D.4)
1)-I
If the sequence xk (n) is then decoded, the decoder output in the range channel
corresponding to a delay of m samples is,
vk(n) = xk (n) . Cm(n)
= [rk(n) - rk-p(n)I Cm(n) (D.5)
From (f). 1) and (D.5) it is seen that interchanging the MTI and decoding operations
has no effect on the output. However, it must be noted that this result is based
on the assumption that the canceller delay is an integer multiple of the code
period. The result is not valid for other delays and for recursive MTI filters.
-D-2
APPENDIX E
OUTPUT OF PROCESSOR-S USTNG DECODERS
In order to demonstrate thle equivalence of Configurations D-5 and D-9,
expressions for their outputs are developed in this Appendix. III the development
that follows, thle delay line canIceller is ignored 'since its effects on the tw.o
configurations are identical . Thle input signal is; denoted by the set of samples
{rii= 0, 1, . . . , KN-l ) where K, is the nmiler of code p~eriods inl the look1
time and - is the niimber of samples inl each code period.
In Configuration D-5, t ie ouitput of the ranlge channel corresponding to a dljay' of
msamples is obtained by multiplying tlI, input by a periodic r-epetitionl of Cm (n
where Cm(.) represents a period of the cede shlifted by in samples. Thu115, 11hc
decoder output is given lby,
K-1
k=O
The Tnth output sample following an) NK sample FF1' is
NK-lY II (in) Y > m y(i) w In(E. 2)
i=D
whie re w e xp (- 2 I'NK).(.
Comnbining (E.1) and (E.2),
Y'ln I-0~) C (i-kN)w i
i=O k=O
.01
LAD-AO94 181 COMPUTER SCIENCES CORP HUNTSVILLE AL F/6 17/9SIGNAL PROCESSOR P0R BINARY PHASE C OOED CR RADAR(U)DEC 77 a K BHAGAVAN DAANO3 76 A 004%
UNCLASSIFIED CSC/TR-77/ 5491 N
Igo__ 2.5
1.8
IIIL25 1.1 1.6±
MICROCOPY RESOLUTION TEST CHART
NATIONAL BURLALI Of STANDARDS 1963 A
Each of the K sequences {U(pn), p = 0, 1, • • . , N-I} is doppler compensated,
i.e.,
j X(p,n) = U(p,n) wnp (E.1O)
The output of the processor in range cell m and doppler cell n is then computed
by decoding followed by summation,
N-1
Vm(n) = X(p,n) Cm(P) (E. 11)[ P=0
N-1= Zp(n) wn p CM(p)
p=O
N-1 K-1= ~ zP(k)wlnk wn p Cm(P)
p=O k=ON-I K-I
=- K zp(k) wnkN wn p Cm(P)
p=O k=O
N-1 K-1= 1: r(kN p) Cm(p) wnp wnkN (E.12)
p=0 k=0
Comparison of (E.5) and (E.12) proves the hypothesis that the outputs of
Configurations (D-5) and (D-9) are identical.
_____ E-3 A
APPENDIX F*
OUTPUT OF PROCESSORS USING PULSE COMPRESSION
Referring to Configuration PC-2 and ignoring the delay line canceller as in
Appendix E, the output of the pulse compression filter in range channel m is
given by
N-1ym(k) = Cm(p)r(kN+p) .(F.1)
p=O
If the K sample FFT o: this sequence is computed, the output sample in the nth
bin is
K-iYm(n) = , Ymk w jnk (F.2)
k-0
Here w1 = exp(-27rj/K)
= WN (F.3)
where
w = exp(-21rj/NK) (F.4)
Therefore,
K-i 11-iYm(n) = 1: Fr(kN+p) Cm(p)wnkN *(F.5)
k0O p=0O
Comparison of (F.5) and (E.12) reveals the similarity between the decoder and the
pulse compression approaches, the only difference being the term due to doppler
compensation.
F-ij
dhAPPENDIX G
CLUTTER GENERATION
It is desired to generate samples of the random clutter components (f1 (i)} and
{fQ(i)) at sampling intervals.of 6. It is assumed that the sequence can be
described by a Gaussian distribution with zero mean and unit variance. These
sequences are required to be highly correlated having Gaussian power spectrum
centered at zero frequency with a standard deviation of aF . Thus, the desired
power spectrum is
Mff(f) 1 exp(-f 2 /2oF 2 ) . (G.I)
Consider a continuous linear system whose impulse response is
g(t) exp(-t2 1or) (G.2)
where
a T 1/ 2 oF . (G.3)
The transfer function of this non-causal system is
G~f) = 1 exp(-f 2/4o2) (G.4)
~G~fa- - F (.42 F
Let the input to this system, denoted n(t), be a zero mean, unit variance, Gaussian
noise process with a flat spectrum,
*nn(f) S fori f < I
0 otherwise . (G.5)
G-1
Then, the output process c(t) is also a zero mean Gaussian process whose power
spectrum is
cc(f)= G(f)2 0nn(f)
= S exp(-f 2 /2G 2) for IfI< L2 F 2S
= 0 otherwise (G.6)
The restriction on the region of existence can be removed if S is chosen to be
small enough such that
* 1 >(G.7)2S,> 20F •
From its power spectrum, it is obvious that if the input noise is sampled at
intervals of S, the samples are independent and have a Gaussian distribution with
zero mean and unit variance. Thus, a discrete equivalent of the continuous system
may be written as,
c(t) = S E n(kS) g(t-kS)
k
If c(t) is sampled at intervals of 6,
c(mS)= S E n(kS) g(m6 -kS)
k
= S. f(m) . (G.9)
c-2
The power spectrum of {f(m)} is,
1,ff(f) Occ (f)
12 exp(-f2 /2a2)2FS. 47roF
1 .2 22exp(-f 12a F) (.10)
where S 2 1 ~ (G.11)
Note that the definition of S satisfies the inequality given in (G.7) and that
the power spectrum of {f(m)} is the same as that of the required clutter
components. Thus, the clutter sequence can be generated using
f(m) = n(kS)g(m6-kS) .(.12)
k
However, it must be noted that the impulse response of the filter has infinite
duration. For implementation in a digital simulation, the impulse response is
truncated to ItI<3S. Since the input noise sampled at intervals of S, six samples
of noise are required in the summation in (G.12). Note however, that several
samples of clutter can be generated from the same six noise samples because the
output sampling interval 6 is much smaller than S. In fact, I samples of clutter
can be computed from six samples of input noise where I S/6.
C-3 1
APPENDIX H
PROGRAM LISTINGS
This appendix contains the listings of all the computer programs developed for
this study. The programs re in FORTRAN and are compatible for execution on the
CDC-6600 computer system.
H-1
IL.BROUTINE ANIT 74/7g. OPT=I FYN 4*2*74355
-. SUBROUTINE ANIT (START)
C**INITIALIZArION FOR NOISE GENERATORS
s- COMMON/RANDM/ARD*RN01,PSARDmSTARTRNDI=START*0*0O0oO1R5'.7'436*0RETURN
I, END
H-
~IBROUTINE CLUTTN 74/74 OPT=l T *#45
C SUBROUTINE CLUTTN(XtSCRtXM29SIGMAFoNCDEL)
C*OGENERATES SAMPLES OF GROUND CLUTTER AND ADDSC**THEM TO THE COMPLEX ARRAY X
5 C**X IS THE INPUT/OUTPUT COMPLEX ARRAY* C**SCR IS THE SIGNAL TO CLUTTER RATIO
C**NOTE==SIGNAL POWER IS ASSUMED TO BE UNITYC*IXM2 IS THE DC TO AC POWjER RATIOC**AC CLUTTER HAS GAUSSIAN SPECTRUM
10 C**WITH ZERO mEANC**SIGMAF IS THE STANDARD DEVIATION OFC**THE CLUTTER SPECTRUMC**NCDEL IS THE RANGE DELAY CORRESPONDINGC**TO THE CLUTTER LOCATION
15COMMON/ADPAR/DELT ,CADVMAXCOMMON/PROPAR/NLOOK ,NSAt4PP ,NFFT ,NSCLK ,NC INTCOMMON/XCODE/NSTAGEINIT(1Oh*FEEDBK(10) ,CODE(1024)COMPLEX X(I)
20; DIMENSION XR(4)tXN(12)* INTEGER CODE
CONST=1,O/(SORT (SCR))NCYCLE=NLOOK/NSAMPPCALL RANDU(XR,2)
25 P1=3*141492654PSI=2*C*PI*XR(2)I CPSI=COS (PSI)SPSI=SIN (PSI)
-y IF(XM2*LT.O) GO TO 20301 60=SQRT(XM2/(1.O*XM2))
GA=SGRT(O.S/(1.O*XM2))GC=GO 'Ci'sG6=G0*SPS ICALL RANDG(XN,12,0*0,1.O)
35 PI2=290*PISIGTAU=1 .O/(PI2*SIGMAF)I SIGSS=SIGTAU/DELTSIGl=SIGSS/l .4142 13562CDEN=O.5/ (SIG1*SI)
401 ITI=1 .253314137*SIGSSTI=FLOAT (ITI)DO 10 IC=19NCYCLED0 11 10=19NSAMPPJ=(IC- )*NSAMPP*ID
45 ICODE=ID-NCDELIF(ICODE.LE.O) ICODE=ICODE.NSAMPPIIOODO 12 1=196
501 M=(6-1)OITI.JB=FLOAT (M)
I EXPT=-DUM *DUM*CDENHMzEXP (EXPT)
55 CI=CI#XN(I)OHM12 CQ=CQ#XN(I.6)*HM
CITEFLOAT(COrJE(ICODE) )*(GC.GA.CI)k H- 3
t UBROUTINE CLUTTN 74/74 OPT=l FYN 4.2*74355
CQT=FLOAT (CODE (ICODE) ) *(GS.GA*CQ)X(J)=Xtj)* CONST*CMPLX(CITCOT)
60 11 CONTINUE10 CONTINUE
RETURN20 CONTINUE
DO 30 IC=1,NCYCLE65 DO 31 ID=1,NSAMPP
JZ (IC-I) *NSAMPP.IDICODE=ID-NCOELIF (ICODE.LE.0) ICODE=ICODE.NSAMPPCIWnFLOAT(CODE(ICODE) )*CPSI
70 CQT=FLOAT(CODE(ICODE) )*SPSIX(J)=X(j)* CONSTOCMPLX(CITCQT)
31 CONTINUE30 CONTINUE
RETURN75 END
H-
SUBROUTINE CORREL 74/74 -OPT=l FTN 4.2*74355
SUBROUTINE CvKELIX*NNzrtNOUTP
C**PULSE COMPRESSION FILTER FOR THEC**PROCESSORS USING PULSE COPdPRESSION
S C**X IS THE COMPLEX INPUT/OUTPUT ARRAYC**NIN IS THE NUMBER OF INPUT SAMPLES
- C**NOUT IS THE NUMBER OF OUTPUT SAMPLES
COMMON/PROPAR/NLOOK ,NSAMPP ,NFFT ,NSCLK ,NC INT10 COMMON/XCODE/NSTAGE,!NIT(k0),FEEDBK(10),CODE(1024)
COMPLEX X(1)9XOUTINTEGER CODENOUT=NIN*NSAMPPNSMPPI1=NSAMPP. 1
is NINP=NIN.1DO 10 II=NINPNOUTI=NOUT-I I NINPXOUT=CMPLX (0.090.0)JF IN= NOUTr- I
20 DO 11 J=1,JFININD=J+I-NSAMPPIF(CODE(J).GT*O)GO TO 12XOUT=XOUT-X (IND)GO TO 11
25 12 XOUT=XOUT.X(IND)11 CONTINUE
X(I)=XOUT10 CONTINUE
DO 20 II=NSMPP1,NIN30 I=NIN-II.NSMPPI
XOU=CMPLX (0.0.0 .0)DO 21 J=19NSAMPPIND=J. I-NSAMPPIF(CODE(J).GTsO)GO TO 22
35 XOUT=XOUT-X(IND)GO TO 21
22 CONTINU*(22 CONTINUTE(ID
X(I)=XOUT40 20 CONTINUE
DO 30 11=19NSAMPPI=NSMPP-I 1.1XOUT=CMPLX (0.0, 0.0)JST=NSAMPP-I .1
4S DO 31 J=JSTNSAMPPIN=J. I -NSAMPPIF(CODE(J).GT.O)GO TO 32XOUT=XOUT-X (IND)GO TO 31
50 32 XOUT=XOUT.X(IND)31 CONTINUE
X(I)=XOUy30 CONTINUE
RETURN55 END
11-5
SUBROUTINE DECODE 74/74 OPT=l FTN 4#2+74355
SUBROUTTNE DECODE(XtNtIR)
CO. IMPLEMENTS THE DECODERC**X IS THE COMPLEX INPUT/OUTPUT ARRAY
s C**N IS THE NUMBER OF SAMPLESC**IR IS THE REQUIRED RANGE BIN
COMMON/PROPAR/NLOOKNSAMPP.NFFT ,NSCLK ,NCINTCOMMON/xCODE/NSTAGEINIT(lO),FEEDBK(IO) ,CODE(1024)
10 COMPLEX Xci)INTEGER CODENCYCLE=N/NSAMPP00 10 1C!,9NCYCLE00 10 1D=1,NSAMPP
15 J=(!C-1)*NSANPP#IDICODE=ID-IRIF(ICODE.LE.O) ICODE=ICODE.NSAMPPIF (CODE(ICODE) .LT*0)X(J)=-X(J)
10 CONTTNUE20 RETURN
END
1 11-6
IUBROUTINE OFT 74/74 OPT=l FTN 4*2+74355
SUBROUTINE DFT(AN.ISNNPIN)
C**COMPUTES THE DISCRETE FOURIER TRANSFORM OFI C**THE COMPLEX ARRAY X5 C**X IS THE COMPLEX INPUT/OUTPUT ARRAY
C**N IS THE NUMBER OF SAMPLES IN XI C**ISN = ;-1 FOR DIRECT DFTC**ISN = *1 FOR INVERSE OFTC**NBIN IS NUMBER OF OUTPUT SAMPLES DESIRED
101 C**IF N = 2**M 9FFT-IS USEDC**OTHERWISE DFT IS USED
COMPLEX A(l),TlT2,TEMP9X(256)P12=6*28318530717959
15 I4ASK=lIGAM=O
1 IGAM=IGAM.1M=20*IGAMIF(N-M)?,4,1
20 4 CONTINUENi =N- 100 20 II=29NI1=11-1IFLIP=O
25 DO 10 J=19IGAMLSN=2** (J-1)
10 IFLIP=2*IFLIP.(MASK.AND.(I/LSN))IF(I.LE.IFLIP)GO TO 2011=1*1
30 12=IFLIP*1TEMP=A (12)A(12)=A(II)A(11)=TEMP
20 CONTINUE35 DO 30 I=1,IGAM
NEL=2#**NEL2=NEL/2NSET=N/NELANG=P 12/NE L
40 SI=SIN(ANG)CI=COS(ANG)DO 30 J=19NSETINCR=(J-1 ) NELSO=0.O
45 C0Z1.ODO 30 II=1,NEL2Jl=II*INCRJ2=J1 .NEL2T1=A(JI)
50 T2=A(J2)*CMPLX(CO#ISN*SO)A(jl)=T1.T2A(J2)=TI-T2SN=SO*CI.CO*SICS=CO*CI-SO#SI
515 CO=CS30 SO=SN
6O TO 100 11-7
SUBROUTINE OFT 74/74 OPT=I FTN 4.2*74355
2 CONTINUEANG2ISN*P12/FLOAT (N)
50 DO 40 I=1,NBINX(I)=CMPLX (0.0,0.0)DO 50 J=1,NARG=ANG*FLOAT( (I-1)*(J-1))T1=CMPLX (O.OtARG)
55 T2=CEXP(TI)
50 ONINUEI)T*AJ40 CONTINUE
DO 60 1=19N70 60 A(I)=XI(I)
100 CONTINUEIF(ISN.GT.O)RETURNDO 110 7=19NA(I)=A(I)/FLOAT(N)
75 110 CONTINUERETURNEND
9UBROUTINE FFTDEC 74/74 .OPT=l FTN 4.2+74355
SUeROUTINE FFTDEC(XNSTARTNSKIPNBINNOUT)
C**FFT PROCESSING FOR THE DECODER APPROACHC**X IS THE COMPLEX INPUT/OUTPUT ARRAY
5 C**NSTART IS SAMPLE WHERE INTEGRATIN BEGINSC**NSKIP SAMPLING RATE REDUCTION FACTORC*oNBIN IS THE NUMBER OF OUTPUT RINS DESIREDC**NOUT = NBIN IN THIS SIMULATION
10 COMMON/PROPAR/NLOOKNSAMPPNFFTNSCLKNCINTCOMPLEX X(1)9XFFT(?56)NS 1IST IN=NSTARTISTOUT=O
15 NOUT=NBIN*NCINTDO 10 INT=19NCINTDO 11 IFFT=19NFFTISAMP=(IFFT-1 ) NSKIP.ISTINXFFT(IFFT)=X(ISAMP)
20 11 CONTINUECALL WEIGHT(XFFT*NFFT)CALL DFT(XFFTNFFT,-1,NBIN)DO 12 IFFT=1,NBINX (IFFT. ISTOUT) =XFFT (IFFT)
25 12 CONTINUEISTOUT=ISTOUT*NBINIST IN=IST IN*NFFT*NSKIP
10 CONTINUERETURN
30 END
H1-9
iUBROUTI NE FFTPC 74/74 OPT=l T **45
SUBROUTINE FFTPC(XoNSTARTvNRIN)
C**FFT PROCESSING FOR PULSE COMPRESSION.C**CONFIGURATIONS
5 C**X IS THE COMPLES INPUT ARRAYC**NSTART SAMPLE AT WHICH INTEGRAT.ION STARTSC**NRIN IS THE NUMBER OF OUTPUT SINS DESIRED
COMMON/PROPAR/NLOOK ,NSAMPPNFFTNSCLK ,NCINT10 COMPLEX X(1)*XFFT(2S6)
NCOH=NFFT*NSAMPPNFIN=NSTART, (NCOH*NCINT)-1DO 10 INT=NSTARTNFINNCOHDO 11 ISAMP=1,NSAMPP
15 DO 12 IFFT=1,NFFTJ=(INT-I )+.(IFFT- ) *NsAt'PP4 ISAMPXFFT (IFFT)=X(J)
12 CONTINUECALL WE-13HT(XFFTgNFFT)
20 CALL DFT(XFFT*NFFT,-1,NBIN)DO 13 IFFT=1,NFFTJ=(INT-j) *(IFFT-1.)*NSAMPP.ISAMPX (J) =XFFT (IFFT)
13 CONTINUE25 11 CONTINUE
10 CONTINUERETURNEND
H- 10
IUBROUTINE FILCAS 74/74 OPT=l FTN 4*2*74355
SUBROUTINE FILCAS(XtNSTARTNFIN)
C*'IMPLEmENTS RECURSIVE DISCRETE FILTERS.C**AS CASCADE OF SECOND AND FIRST ORDER SECTIONS
5 C**CANONICAL REALIZATION IS USEDC**X IS THE COMPLEX INPUT/OUTPUT ARRAYC**NSTART IS SAMPLE WHERE FILTERING BEGINSC**NFIN IS SAMPLE WHERE FILTERING ENDS
10 COMMON/FLTT/NSECNFIRSTNTYPE(10),CSEC(2,10),CFIRSTCONSTCOIMON/PROPAR/NLOOK ,NSAMPPNFFTNSCLK ,NCINTLOGICAL NTYPECOMPLEX X(1),Y(3),DUMDO 10 IsEC=1,NSEC
15 DO 11 1=19311 Y(I)=(O.09O.O)
DO 12 I=NSTARTvNFINS(1) =X (I)D0 13 IF-492
20 13 Y(1)=Y(l)-CSEC(IFgISEC)*Y(IF*1)DUM=Y (1)*V( 3)IF(NTYPE(ISEC))6O TO 15DUMgDUM-Y (21-V (2)GO TO 16
25 15 DUM=DUMY(2)*Y(2)16 CONTINUE
X(I)=DUMY(3)=Y(?)Y(2)=Y(l)
30 12 CONTINUE10 CONTINUE
IF(NFlRST*EQ.O)GO TO 25Y(1)=(0O,0.0o)Y(2)=(0.,O.O*)
35 DO 22 I=NSTARTNFINY(1)=X(I)Y(1)=Y(1)-CFIRST*Y (2)IF(NTYPE(NSEC+1))GO TO 23DUMVY(l)-Y(2)
.0 GO TO2423 DUM=Y(1)*Y(2)24 CONTINUE
X(I)DUmY(21)Y(1)
5 22 CONTINUE25 CONTINUE
DO 30 I=NSTARTNFIN30 XMI=XCI)*CONST
RETURNo END
LBROU71NE INTDEC 74/74 OPT=l FTN 4.2+74355
I SUBROUTINE INTDEC(XvNBIN)
COOINTEGRATION FOR THE DECODER APPROACH
5 COMMON/PROPAR/'NLOOK ,NSAMPR ,NFFT ,NSCLK ,NC NT* COMPLEX X(I)
DO 10 IFFT=1INI* SUMO.0O
La" DO 12 INT=19NCINT10 ISAMP=(INT-l).NBIN*IFFT
SUM=SUM#CABS (X (ISAMP) )**212 CONTINUE
X(IFFT)=CMPLX(SUM9O.O)10 CONTINUE
is RETURNEND
H-1~2
T
SUBROUTINE INTPC 74/74 OPTz) FIN 4.2#74355
SUBROUTINE INTPC(XNSTART)
C**NON COHERENT INTEGRATION FOR THECOOPlILSE COMPRESSION APPROACH
5COMMON/PROPAR/NLOOKNSAMPPNFFTNSCLKNCINTCOMPLEX Xtl)*XINTNCOH=NFFT*NSAMPP00 10 I=19NCOH
10 XINT=CMPLX(O.OO.O)DO 11 INT=19NCINTJ=(NSTART-1) .I*(INT-1)*NCOHXINT=XINT*X (JI
11 CONTINUEi5 X(I)=XINT
10 CONTINUERETURNEND
k __H - 13
SUBROUTINE MTI 74/74 -OPT=1 FYN 4.2.74355
SUBROUTINE 9411(XNINNPERNPULSENOUT)
COOIMPLEMENTS THE DELAY LINE CANCELLERC**X IS THE COMPLEX INPUT/OUTPUT ARRAY
s C**NIN IS THE NUMBER OF INPUT SAMPLESC**NPULSE IS NUMBER OF PULSE CANCELLEDC**NPER IS NUmHER OF CODE PERIODS IN DELAYC**NOUT IS NUMBER OF OUTPUT SAMPLES
LO I COMMON/PROPAR/NLOOK ,NSAMPPNFFTNSCLK.NCINTCOMPLEX XSTORE(I50)9YSTORE(I50),X(1)
I IIN=NINNDELAY=NSAMPP*NPERDO 15 IFILT=1,NPULSE
is tOUT=MIN#NDELAYDO 10 I1,NDELAYXSTORE(I)=X(I)
10 CONTINUENDELI=NDELAY.1
29 DO 11 h=NDEL1,MINtNDELAYDO 12 J=19NDELAYYSTORE(J)=X(I*J-1)
12 CONTINUEDO 13 J=19NDELAY
25 X(I*J-1)=YSTORE(J)-XSTORE(J)13 CONTINUE
DO 14 Jd.#NDELAYXSTORE (J) =YSTORE (J)
14 CONTINUE30 11 CONTINUE
MINP=MIN.I00 16 J=MINPqMOUTX (J) =-YSI ORE (J-MIN)
16 CONTINUE35 MIN=MOUT
15 CONTINUENOUT=MOuTRETURNEND
H- 14
SUBROUTINE NOISE 74/74 OPT=l FTN 4.2*74355
C*'ADDS NOISE TO THE INPUT SIGNALC**X IS THE COMPLEX INPUT/OUTPUT ARRAY
SCOMMON/xNOISE/XME AN, STDEVCOMMON/PROPAR/NLOOK ,NSAMPPNFFTNSCLK .NC INTDIMENSION XU(21.)
I COMPLEX X (I) GAUSS,10[ DO 10 1=19NLOOK
CALL RANDU(XU924)GAUSS 1=0.0GAUSS2O.O0D0 11 J.=912
is. GAUSSI=GAUSS1.XU(J)11 GAUSS2=GAUSS2*XU(J.12)
GAUSSl= (GAUSS1-6*O) *STDEV*XMEANGAUSS2=(GAUSS2-6.O)*STDEV*XMEANGAUSS=Cih?,LX (GAUSS 1 ,AUSS2)
20 10 X(I)=X(I?.GAUSSRETURNEND
H-15
~LBROUTINE PLOTIP ?4? OP= FIN 4.2+74355
SUBROUTINE PLOTIP(XMXMSKIPXMPMSIZEFRMKPERIO)
C*OGENERATES A LINE PRINTER PLOT
S DIMENSION X(1),XL(10)9W(6)DATA ELANKASTRIX9HORVERT/IH 91I4@,1H-91HI/I DATA W(1)/IOH(1XI592Xt/DATA W(3)/3HAl,/DATA W(4)/9H1XE12*6)/
10 ~ C PERIODIC PLOTC X=ARRAY TO BE PLOTTEDc MXwSTARTING ADDRESSC MSKIPX=DISTANCE BETWEEN POINTSC MP z NUMBER OF POINTS PLOTTED
i5 C MSIZE =WIDTH OF THE PLOT(ESS THAN 110)C R = "I4SIZE"C KPERIO = PERIOD
WRITE (6, 1)1 FORMAT(JI)
20 IF(MSIZE.GT*110) MSIZE=11OIF (MSIZE.GE*11O)FRM=3H110W(2)=FRmMMXUMX *MP- IMA=MX
25 IF(MA*LE.O) MA=MA+KPERIOXMIN=X (mA)XI4AX=X (MA)DO 5 JJ=mxMMXomsKIPXJ=JJ
30 IF(J*LEO) J=J*KPERIOIF(J.GT.KPERIO) J=J-KPERIOIF(X(J),GT.XMAX) XMAX=X(J)IF(X(J).LT.XMIN) XMIN=X(J)
S CONTINUE35 IF((XMAX-XMIN).LE.1.E"7)XMIN=XMIN-1.E-5
KS5lIF(XMIN.GT.O.O.OR.XMAX.LT.0O0) KS=?DELX (XIAX-XMIN)/FLOAT (MSIZE-1)GO TO (798)*KS
4.0 7 NAXIS=1.0-XMIN/DELX8 CONTINUE
DO 13 JA=MX*MMXMSKIPXJX=JAIF(JX.LE.O) JX=JX#KPERIO
45 IF(JX*GT.KPERIO) JX=JX-KPERIO00 14 J=19MSIZE
14 XL(J)=BLANKIF(KS*Eo.1) XL(NAXIS)zVERYIX=1*0. (X (JX)-XMIN)/nELX
50 IF(IX.GT.MSIZE) IX=MSIZEIF(IX.LTol) IX21GO TO (?1922)tKS
21 IF(IX.LF*NAXIS) GO TO 23NAXISP=NAXIS.1
ss DO 24 I=NAXISP*IX?4 XL(I)=AsTRIX23 IF(IX*NF*NAXIS) GO TO ?5
____________________________H-16 _____
sJUBROUTINE PLOTIP 74/74 .OPT=l FTN 4.2.74355
XL(IX)=ASTRIXGO TO 26
6c 25 NAXISM=NAXIS-1DO 27 I=IX*NAXISM
27 XL(I)=ASTRIXGO TO 26
22 IF(XMIN.GT.O.) GO To 3065 DO 31 I=IXMSIZE
31 XL(I)=ASTRIXGO TO 26
30 DO 28 1=191X28 XL(I)=AsTRIX
7026 CONTINUEWRITE (6,W)JA, (XL(I) ,1=1,MSIZE)tX(JX)
13 CONTINUERETURNEND
11-17
IUBROUTINE PNCODE 74/74 -OPT=I FTN 4.2*74355
SUBROUTINE PNCODE
C**GENERATION OF THE PSEUDO RANDOM SEQUENCE
5 COMHON/PROPAR/NLOOKNSAMPPNFFTNSCLKNCINTCOMMON/XCODE/NSTAGE, INIT (10) ,FEEDBK (10) ,CODE (1024)
4 DIMENSION RGSTR(10)INTEGER FEED8KCODERGSTR0O 10 I=lNSTAGE
10 10 RGSTR(I)=INIT(I)DO 1 ICODE=INSAMPPNSCLKKBACK=0DO 2 1=1,NSTAGEKBACK=K8ACK*FEEDBK (I) *RGSJT(I)
152 CONTINUEKBACKH=KBACK/2ICODEP JCODE*NSCLK-1DO 4 JCODE=ICODEICOOEPCODE (JCODE) =RGSTR (NSTAGE)
20 4 CONTINUEDO 3 J-?,NSTAGEI=NSTAGE+2-JRGSTR(I)=RGSTR(I-1)
3 CONTINUE25 RGSTR (1)=KBACK-2*KBACKH
1 CONTINUERETURNEND
H- 18j
JJBROUTINE WUANT 74/74 OPT=1 FTN 4.2+74355
C*6OUANTIZATION == A/D CONVERSION
5 COMMON/ADPAR/DELTOADVMAXCOMMON/PROPAR/NLOOKNSAMPPNFFTNSCLK ,NCINT
I COMPLEX X(I)DO 10 I=1,NLOOK
10 XA=REAL(X(l))X8=AIMAG(X(I))AX=ABS (XA)BX=ABS (XB)IAX=AX/oAD
i5 !6X=BX/oADAY=OAD* (FLOAT (IAX) .0.5)BY=OAD* (FLOAT (IBX)# .S)XI=SIGN(AYXA)XQ=SIGN (BYtXB)
20 X(I)=CMPLX(XIXO)10 CONTINUE
RETURNEND
H1-19
I
SUBROUTINE RANDG 74/74 OPT=I FTN 4*.274355ISUBROUTINE RANDG(X,N,XMEANSTDEV)
, J C**GENERATES GAUSSIAN RANDOM NUM8ERSC**N IS THE NUMBER OF NOISE SAMPLES
5 C**X IS THE OUTPUT ARRAYC**XMEAN IS THE MEAN OF THE NOISE SEQUENCEC**STDEV IS THE STANDARD DEVIATiONC**OUTPUT IS AN INDEPENDENT SEOUENCE
101 DIMENSION X(1),XU(12)DO 10 I=I,NCALL RANDU(XU912)GAUSS=O.ODO 11 J=1,12
15 11 GAUSS=GAUSS*XU(J)I GAUSS=(GAUSS-6.O) STDEV*XMEAN10 X(I)=GAUSS
RETURNI END
II
1
11-20
SUBROUTINE RANDU 74/74 -OPT=l FTN 4,2#74355
SUBROUTINE RANDU(X*N)
C*.C'ENERA1ES uNIFORMLY D1STRIBUTEDC**RANDOM NUJMRERS
5 C**N IS THE NtUMBER OF NOISE SAMPLESC**X IS THE OuTPUT ARRAY
I C**OUTPUT IS AN INDEPENDENT SEQUENCE
COMMON/RANDM/ARDRND1 ,RS101 DIMENSION X(1)
DO 3 I11NARN=ARD**2*RS**2K=ARN/1 000000000.ARD0 (ARN-FLOAT (K) *1000000000.) /1000.
15 IF(ARD)2*192I ARD=1*O2 RS=RS.1
RND=ARD*O.0000013 X(I)=PND
20 RETURNEND
H-2 1
.
JUBROUTINE RMS 74/74 OPT=l FTN 4.2.74355
ISUBROUTINE M(*SATC*ECOMPUTES THE RMS VALUE OF EACH SAMPLE OF51 C**THE COMPLEX ARRAY X
5 C**RESULT IN REAL PART OF ARRAY X
I COMPLEX X(l)COMMON/PROPAR/NLOOKNSAMPPNFFTNSCLK ,NCINTNCOH=NFFT*NSAMPP
101 NFIN=NSTART. (NCOH*NCINT)-iDO 10 I=NSTART9NFINSSQ=CABS(X(I))X(Ih-CMPLX(SSQ900O)I10 CONTINUE
15 RETURNEND
A 11-22
JJBROUTINE SI6NAL 74/74 OPT=l FTN 4.2.74355
I SUBROUTINE SIGNAL(X
C**GENERATES SAMPLES OF SYNTHETIC VIDEO5! C*.INCLUOES TARGET RETURNCLUTTER AND NOISE
C**CLUTTER INCLUDES IN RANGE CLUTTERC**OUT OF RANGE DISTRIBUTED CLUTTERC**FIXED CLUTTER9 ANTENNA SPILLOVERC**AND OTHER ISOLATED CLUTTER
to COMPLEX XCI)COMMON/SIMPAR/NMONTEINOPT(7),IPRINT(lO)COMMON/pROPAR/NLOOK ,NSAMPPNFFTNSCLKNCINTCOMMON/SI GPAR/FDOP ,NDELTACOMMON/CLTPAR/SCRI.SCRDSCRFSPILSIGMAFXM2,NCDELAXM2OSIGMAO
I5 v NCDELO*SCRO
DO 10 1=19NLOOK10 X(I).=CMPLX(0.OO.O)
IF(JINOPT'C1)eEO.1)CALL TARGET(X)IF(INOPT(2)*EQ91)CALL NOISE(X
?of IF(INOPT(3)*EO*O)GO TO 11CALL CLUTT(XSCRIXM2,SIGMAFNDELTA)
11 IF(INOPT(4.EQ.O)GO TO 12DO 13 ICELL=1,NSAMPPfNSCLKIRANG= (ICELL-1) /NSCLK
5 DENOM=1.O0.015*FLOAT(IRANO)WEIGHT= (I .0/DENOM) *03SCRDR=SCRD*3 .4/WEIGHTCALL CLUYT(XSCRDRXM2,SIGMAFICELL)
13 CONTINUE30 f12 IF(INOPT(5)*EQ*O)GO TO 14
CALL CLUTT(XSCRF,-1.O9,ONCDELA)14 IF(INOPT(6)*EQ*O)GO TO 15
CALL CLU)TT (XSCR0,XM2OSIGMAONCDELO)15 IF(INOPT(7)*EQ.O)GO TO 16
35 CALL CLUTT(X9SPIL9-I..O O,*0O)16 CONTINUE
RETURNEND
11-23_
SUBROUTINE SPCTRM 74/74 OPT=I FTN 4.2+74355
SUBROUTINE SPCTRM(XNNPLOTIOPT)
C**COMPUTES AND PLOTS THE SPECTRUM OF XC**X IS THE COMPLEX INPUT ARRAY
5 C**N IS THE NUMBER OF SAMPLES IN XC**IOPT =1 FOR MAGNITUDE PLOT ONLYC**IOPT = 2 FOR PHASE PLOT ONLYC**IOPT = 3 FOR BOTH PLOTS
101 COMPLEX X(l),Y(1024)DIMENSION PLOT(1024)DATA FRm/3H100/
j DO 10 1=19N10 Y(I)=X(I)
15 CALL DFT(YN,-IN)P1=39141592654P12=Pl/?.0NP2=NPLOT/2NP2P=NP2. 1
20 NP2M=NP2- 1IF(IOPT.EQ.2)GO TO 15DO 20 I=19NP2P
20 PLOT(I+NP2M)=CABS(Y(I))DO 21 I=19NP2M
25. 21 PLOT(I)=CABS(Y(N.I-NP2M))CALL PLOTIP(PLOT,1,1,NPLOT,100,FRMNPLOTIIF (IOPT.EO 1) RETURN
15 CONTINUEDO 30 I=19NP2P
30 YR=REAL(Y(l))YI=AIMAc,(Y(I))IF(ABS(YR).LT*1.OE-09)GO TO 31PLOT(I*NP2M)=ATAN2(YI .YR)GO TO 30
35 31 PLOT(I.NP2M)=SIGN(PI2,YI)30 CONTINUE
DO 40 I=1,NP2MYR=REAL (Y (N*I-NP2M))YI=AIMA6~(Y (N4I-NP2M))
40 IF(AfS(YR)*LT*1.OE-09)GO TO 41PLOT (I)=ATAN2 (YIYR)6O TO 40
41 PLOT(I)=SIGN(P12,YI)40 CONTINUE
45 CALL PLOTIP(PIOT,1,1,NPLOT,100,FRMNPLOT)RETURNEND
low1H-24
SUBROUTINE START 74/74 OPT=l FTN 4.2*74355
I SUBROUTINE START
C**INITIALIZATION SUBROUTINEC**ALL THE PROGRAM INPUTS ARE READ IN NAMELIST
5 C**ARDRND1,RS ARE INITIALIZATION PARAMETERS FORC**THE NOISE GENERATORSC**NBIT IS THE WORD LENGTH OF A/D CONVERTERC**FSAMP IS THE SAMPLING FREQUENCYC**NSCLK = I IN THIS SIMULATION
io C**VMAX IS HALF THE DYNAMIC RANGE OF A/D CONVERTERC**SNRDB IS SIGNAL=TO=NOISE RATIO IN DSC**NSEC IS NO. OF SECOND ORDER SECTIONS IN THECO*RECURSIVE NOTCH/LP FILTERC**NFIPST IS I IF ORDER OF FILTER IS ODD
15 C**OTHERWISE NFIRST IS ZEROC**NTYPE TYPE OF EACH SECOND ORDER AND FIRSTCO*ORDER SECTION LOGICAL ARRAYC**,TRUE, FOR LP AND ,FALSE. FOR HP FILTERC**NOTE==ONLY BUTTERWORTH AND CHEBYSHEV FILTERS
201 C**CAN BE IMPLEMENTED IN THIS SIMULATIONC'*FDOP IS THE DOPPLER FREOUENCY OF TARGETC**NDELTA IS THE TARGET RANGE BIN NUMBERC*eNSTAGE IS NO, OF STAGES IN THE PN SEQUENCE GENERATORC*OINIT IS THE INITIAL CONTENTS OF SHIFT REGISTER
25 C**FEEDBK IS THE FEEDBACK CONNECTION FOR 'HEC**SHIFT REGISTER GENERATORC**NFFT IS THE NUMBER OF COHERENT INTEGRATION SAMPLESC**NCINT = I IN THIS SIMULATIONC**NMONTE IS NOT USED IN THIS SIMULATION
30 C**INOPT IS THE INPUT OPTION ARRAYC**INOPT(1)=I = TARGET IS PRESENTC*4INOPT(2)=l = NOISE IS PRESENTC**INOPT(3)=I = IN RANGE CLUTTER PRESENTC*oINOPT(4)=1 =DISTRIBUTED CLUTTER IS PRESENT
35 C**INOPT(S)=l = FIXED CLUTTER IS PRESENTC**INOPT(6)=I = OTHER CLUTTER IS PRESENTC**INOPT(7)=l =ANTENNA SPILLOVER IS PRESENTC**IPRINT IS NOT USED IN THIS SIMULATIONC*.ss'"'SCR STANDS FOR SIGNAL TO CLUTTER RATIO"""
40 C¢*SCRDBI IS sCR FOR IN RANGE CLUTTER IN DBC**SCRDBD IS SCR FOR DISTRIBUTED CLUTTER IN DBC**SCRDBF IS SCR FOR FIXED CLUTTER IN DBC *SCRDBO IS SCR FOR OTHER CLUTTER IN DRC**SPILDB IS ANTENNA SPILLOVER IN DB
45 C**NCDELA IS RANGE BIN OF FIXED CLUTTERC**SIGMAF IS THE CLUTTER SPREAD FOR IN RANGEC**AND DISTRIBUTED CLUTTERSC**XM2 IS THE CLUTTER DC TO AC ROWER RATIO FORC**IN RANGE AND DISTRIBUTED CLUTTER
501 C**NCDELO IS RANGE BIN OF OTHER CLUTTERC**SIG?4A0 IS SPREAD OF OTHER CLUTTERC*eXM20 IS DC TO AC POWER RATIO OF OTHER CLUTTER
COMMON/ADPAR/DELT90ADqVMAXCOMMONPANDM/ARDRNDRS
I COMMON/XNOISE/XMEANSTDEV
COMMON/FLTT/NSECNFIRSTNTYPE(lO),CSEC(2,1O),CFIRSTCONST
11-25
SUBROUTINE START 74/74 -OPThI FTN 492#74355
COMMON/xCODE/NSTAGE, INIT (10) ,FEEORK (10) ,COOE (1024)COMMON/PROPAR/NLOOKNsAMPPNFFT ,NSCLKNCINT
60 COMMON/s IGPAR/FOOPNDEL TACOMMON/SIMPAR/NMONTE, INOPT (7) ,lPRINT (10)COMMON/CLTPAR/SCRISCRDSCRFSPILSIGMAF,XM2,NCOELAKM20,SIGMAOoNCOEL09SCRO
INTEGER FEEOBKvCODE65 LOGICAL NTYPE
NAMELIST/RNDGEN/ARDRND1 ,RSNAMEL 1ST/AD/NB IT ,FSAMPNSCLKVMAXNA#4E1I ST/NO IS/SNRDRNAMELIST/FLT/NSE:CNFIRSTNTYPECSECCFIRSTCONST
70 NAMELIST/SIG/FDOPNDELTANAMEL IST/PNC/NS1'AGE, IN1l ,EEEDBKNAMELIST/PRO/NFFT ,NCINTNAMELIST/SIM/NMONTE91 NOPT,1PRINTNAMELIST/CLT/SCRDB! ,SCRDROSCRO8FSCRDOSPILDANCDELASlGMAr,
75 *XM2*NCDEL0,SIGMAO*XM20
NAMELIST/PRINT/NBITFS4PNSCLKVM4AXSNRD8,FDOPNOELTANSTAGE,I INITFEEDBKNFFTNCINTNMONTEINOPTIPRINTSCRDBISCRDBD,2 SCRDBFSCRDB0,SPILDoNCDELASIGMAF*XM2,NCDELOSIGMA0,XM203,NSECNFIRSTNTYPECSECCFIRSTCONSTARD.RND1 ,RS
80 READ(59AD)READ (59RNDGEN)READ (5SNO I S)READ (5#FLT)READ (59SIG)
85 READ (5,PNC)READ (5,PRO)READ(59SIM)READ (5.CLT)WRITE (6 ,PRINT)
90 DELW1,*O/FSAMP
SCRI=10wE (O*1*SCRDBI)SCRD=10*E (0. 1SCRD8D)
SCRF=1O*0(O.I*SCRDBF)I95 SCRO=10*0(0*1*SCRDRO)
SPIL=lO** (0, 1*SPILDP)SNR=10* (0. 1*SNRDB)VAR=1 .0/SNRSTDEV=SQRT (VAR/2,0)
00 XMEAN=0.0LENGTH1 (2**NSTAGE)..I
- NSAMPPLENGT4*NSCLKNCYCLE=NFFT*NCINT+SNLOOK:NCYCLE*NSAMPP
05~ CALL PNCODEDO 10 1=1,NSAMPP
10 CODE(I)=2*CODE(I)-lRETURNEND
H-26
JUBROUTINE TARGET 74./74 OPT=I FTN 4o2#74355
I SUBROUTINE TARGET (K)
C**ADDS SAMPLES OF TARGET RETURN TO INPUT ARRAY51 C4'X IS THE COMPLEX INPUT/OUTPUT ARRAY5 C**TARGET IS ASSUMED TO BE NON FLUCTUATING
C**TARGET RETURN POWER IS UNITY
COMMON/ADPAR/DELT ,OADtVMAXCOMMON/PROPAR/NLOOK ,NSAMPPNFFT ,NSCLKNCINT
101 COMMON/XCODE/NSTAGEINIT(1O),FEEDBK(1O),CODE(1024)I COMMON/S IOPAR/EDOPo'NOELTA
COMPLEX X(I)I DIMENSION XR(4)I INTEGER CODE
i5 TPIn6*283185307CALL RANDU(XR94)I PSI=XR(2) *TPIOMOOP=FDOP*TP ITI ME=0 .0
201 NCYCLE=NLOOK /NSAMPPDO 10 1C=1,NCYCLEDO 11 10=1,NSAMPPJ=(IC-I) 'NSAMPP.ID!COOE=ID-NDELTA
25 IF(ICODE.LE*0) ICODE=ICODE*NSAMPPARG=T IME*OMDOP.PSIXI=FLOAT(COOE(ICODE))*COS(ARG)XQ=FLOAT (CODE (ICODE) )*5SJ (ARG)X(J)=X(J).CMPLX(XI#XO)
30 11 TIME=TIME.DELT10 CONTINUE
RET URNEND
H1-27
JJBROUTINE TAYWG 74/74 OPT=l FTN 492+74355
I SUBROUTINE TAYWG (X*NLOOK)
C**IMPLEMENTS TAYLOR WEIGHTING FOR ANALOG PROCESSORS ~CO.L SNME O APE N*X IN THE COMPLEX INPUT/OUTPUT ARRAY
COMPLEX X(I)I DIMENSION F(9)DATA F/.462719,.126816E-1,.302744E-2,-.178566E-2,.884107E-3,
10 *-323E39247-9-477E5-297E4N=13500N2=N/2DELANG=6. 283185307/NI DO 10 K=19NLOOK
15 WEIGHT=1.0DO 20 M=199IN=*K--2ANG=DELANG* INC
20 WEIGHT=wEIGHT*F(M)*COS(ANG)*2,0201 10 X(K)=X(K)OWEIGHT
RETURN
END
H-2
rIROUTINE WEIGHT 74/74 OPT=3 FTN 4.2*74355
I SUBROUTINE WEIGHT(X9N)
C**HAMMING WEIGHTING PRIOR TO FFT PROCESSING
5 DIM'ENSION XOJ)COMPLEX XN2=N/2PI=3. 141592654DELANG=PI/FLOAT (N)
101 ANG=-PI3 00 10 1=19N
ANG=ANG+DELANGWIND=O.54*O.46*COS (ANG)I X(I)=X(I)*WIND
1s 10 CONTINUERETURNI END
H-2%wm -
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